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Groups of transformations of Riemannian manifolds. (English. Russian original) Zbl 0735.53026

J. Sov. Math. 55, No. 5, 1996-2041 (1991); translation from Itogi Nauki Tekh., Ser. Probl. Geom. 22, 97-165 (1990).
Introduction: We consider the articles reviewed by R. Zh. Mat. from January 1971 through August 1989 on transformation groups of Riemannian manifolds and their applications. Further references can be found in surveys and monographs [B. A. Dubrovin, S. P. Novikov and A. T. Fomenko, Modern Geometry. Methods and applications, 2nd rev. ed. Moscow: Nauka (1986; Zbl 0601.53001); I. P. Egorov, Itogi Nauki Tekh., Ser. Probl. Geom. 10, 147–191 (1978; Zbl 0405.53010); A. Z. Petrov, New methods in the general theory of relativity. Moscow: Nauka (1966; Zbl 0146.23901); N. S. Sinyukov, Geodesic mappings of Riemannian spaces (Moscow 1979; Zbl 0637.53020); A. P. Shirokov, Itogi Nauki Tekh., Ser. Probl. Geom. 12, 61-95 (1980; Zbl 0479.53025); S. Kobayashi, Transformation groups in differential geometry. Berlin etc.: Springer-Verlag (1972; Zbl 0246.53031); S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 1. New York etc.: Interscience Publishers (1963; Zbl 0119.37502); Vol. 2 (1969; Zbl 0175.48504); A. Lichnerowicz, Geometry of groups of transformations. Leyden: Noordhoff (1977; Zbl 0348.53001); K. Yano, Ber. Math. Forsch.-Inst. Oberwolfach 4, 339–351 (1971; Zbl 0221.53050)]. The articles considered in these publications are as a rule not included in the present article.
Taking account of the large number and diversity of applications, we have made it our goal in this survey to enumerate the principal directions and methods of applied investigations. A substantive description of them would require a much larger framework. The numerous papers on automorphism groups of complex, Kähler, and contact structures remain beyond the scope of this paper, as do articles on transformation groups of Finsler manifolds, which should be the object of a separate study.

MSC:

53C20 Global Riemannian geometry, including pinching
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
57S25 Groups acting on specific manifolds
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References:

[1] B. Abakirov, ?Some transformation groups in Riemannian spaces with degeneracy fields,? in:Studies in Topology and Geometry [in Russian], Frunze (1985), pp. 3?6.
[2] B. Abakirov and D. Moldobaev, ?Some problems about groups of conformai mappings of Riemannian spaces,?Sb. Tr. Aspirantov i Soiskatelei (Collection of Papers by Graduate Students and Research Assistants), Kirg. Univ. Ser. Mat. Nauk,10, 3?7 (1973).
[3] G. B. Abakirova, ?On intransitive groups of conformai mappings in four-dimensional spaces with degeneracy fields,? in:Studies in Topology and Geometry [in Russian], Frunze (1985), pp. 6?14.
[4] D. V. Alekseevskii, ?Groups of conformai mappings of Riemannian spaces,?Mat. Sb.,89, No. 2, 280?296 (1972).
[5] D. V. Alekseevskii, ?S n andE n are the only Riemannian spaces admitting an essential conformai mapping,?Usp. Mat. Nauk,28, No. 5, 225?226 (1973).
[6] D. V. Alekseevskii, ?Holonomy groups and recurrent tensor fields in Lorentz spaces,?Prob. Teorii Gravitatsii i Elementarn. Chastits (Problems of Gravitational and Elementary Particle Theory), No. 5, Atomizdat, Moscow (1974), pp. 5?17.
[7] D. V. Alekseevskii, ?Homogeneous Riemannian spaces of negative curvature,?Mat. Sb.,96, No. 1, 93?117 (1975). · Zbl 0325.53043
[8] D. V. Alekseevskii and B. N. Kimel’fel’d, ?The classification of homogeneous conformally flat Riemannian manifolds,Mat. Zametki,24, No. 1, 103?110 (1978).
[9] G. B. Alybakova, ?On intransitive groups of conformai mappings of four-dimensional Riemannian spaces with degenerate hypersurfaces,? in:Studies in Topology and Generalized Spaces [in Russian], Frunze (1988), pp. 63?70.
[10] A. V. Aminova, ?On gravitational fields admitting groups of projective motions,?Dokl. Akad. Nauk SSSR,197, No. 4, 807?809 (1971). · Zbl 0239.53018
[11] A. V. Aminova, ?Projective groups in gravitational fields. I,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 8, 3?13 (1971). · Zbl 0239.53018
[12] A. V. Aminova, ?Projective groups in gravitational fields. II,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 8, 14?20 (1971). · Zbl 0239.53018
[13] A. V. Aminova, ?On infinitesimal mappings that preserve the trajectories of test bodies,? [in Russian], Preprint ITF-71-85 R.-Kiev (1971).
[14] A. V. Arninova, ?Projective-group properties of some Riemannian spaces,?Tr. Geometr. Seminara, VINITI,6, 295?316 (1974).
[15] A. V. Aminova, ?Groups of projective and affine motions in spaces of the general theory of relativity,?Tr. Geometr. Seminara, VINITI,6, 317?346 (1974).
[16] A. V. Arninova, ?Projective groups in space-times admitting two constant vector fields,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 10?11, 9?22 (1975?1976).
[17] A. V. Aminova, ?On concircular motions in Riemannian spaces,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 10?11, 127?138 (1975?1976).
[18] A. V. Aminova, ?The determination of infinitesimal almost projective mappings,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 13, 3?9 (1976).
[19] A. V. Aminova, ?Concircular vector fields and group symmetries in universes of constant curvature,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 14?15, 4?16 (1978).
[20] A. V. Aminova, ?Examples of groups of almost projective motions,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 14?15, 138?142 (1978).
[21] A. V. Aminova, ?Groups of almost projective motions of spaces of affine connection,?Izv. Vuzov, Mat., No. 4, 71?75 (1979).
[22] A. V. Aminova, ?Groups of almost projective motions in reducible gravitational fields,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 17, 3?11 (1980).
[23] A. V. Aminova, ?On a class of projectively movable spaces. I,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 18, 3?10 (1981).
[24] A. V. Aminova, ?On skew-orthogonal frames and certain properties of parallel tensor fields on Riemannian manifolds,?Izv. Vuzov. Mat., No. 6, 63?67 (1982). · Zbl 0509.53019
[25] A. V. Aminova, ?On a moving skew-orthogonal frame and a type of projective motion of Riemannian manifolds,?Izv. Vuzov. Mat., No. 9, 69?74 (1982). · Zbl 0511.53020
[26] A. V. Aminova, ?On the Eisenhart equation and the first integrals of the equations of geodesies in Riemannian manifolds of Lorentz signature,?Izv. Vuzov. Mat., No. 1, 12?26 (1983). · Zbl 0514.53017
[27] A. V. Aminova, ?On the projective-group properties of Riemannian spaces of Lorentz signature,?Izv. Vuzov. Mat., No. 6, 10?21 (1984). · Zbl 0551.53015
[28] A. V. Aminova, ?Nonhomothetic projective motions in ordinaryh-spaces of Lorentz signature,?Izv. Vuzov. Mat., No. 4, 3?13 (1985). · Zbl 0581.53014
[29] A. V. Aminova, ?Lie algebras of projective motions and mechanical conservation laws in two-dimensional universes of special structure,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 22, 3?12 (1985).
[30] A. V. Aminova, ?A surface of revolution as a dynamic model of a Lagrangian system with one degree of freedom. Conserved quantities,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 22, 12?30 (1985).
[31] A. V. Aminova, ?Lie algebras of projective motions in h-spaces of type (3),?Izv. Vuzov. Mat., No. 3, 68?71 (1987). · Zbl 0628.53021
[32] A. V. Aminova, ?On the projective-group symmetries of Friedman universes and their multidimensional generalizations?ordinaryh-spaces of type {1(1...1)},?Izv. Vuzov. Mat., No. 12, 66?68 (1987).
[33] A. V. Aminova, ?On the integration of a first-order covariant differential equation and geodesic mappings of Riemannian spaces of arbitrary signature and dimension,?Izv. Vuzov. Mat., No. 1, 3?13 (1988). · Zbl 0649.53009
[34] A. V. Aminova, ?Symmetry groups in the general theory of relativity,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 25, 16?23 (1988).
[35] A. V. Aminova, ?Lie algebras of projective motions of ordinaryh-spaces of Lorentz signature,?Izv. Vuzov. Mat., No. 1, 3?12 (1989). · Zbl 0681.53013
[36] A. V. Aminova, ?On invariance groups of the equations of motion of test bodies of isotropic cosmological models,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 26, 93?101 (1989).
[37] A. V. Aminova and Yu. V. Monakhov, ?The unified nonsymmetric field theories of Einstein, Bonnor, and Schrödinger in a space with symmetries,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 12, 3?16 (1977).
[38] A. V. Aminova and A. M. Mukhamedov, ?Groups of almost projective motions in De Sitter space,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 16, 3?8 (1980). · Zbl 0482.53017
[39] A. V. Aminova and A. M. Mukhamedov, ?Groups of almost projective motions ofn-dimensional (pseudo)-Euclidean spaces,?Izv. Vuzov. Mat., No. 11, 5?11 (1980). · Zbl 0482.53017
[40] A. V. Aminova and T. P. Toguleva, ?Projective and affine motions determined by concircular vector fields,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 10?11, 139?153 (1975?1976).
[41] V. V. Astrakhantsev, ?On holonomy groups of four-dimensional pseudo-Riemannian spaces,?Mat. Zametki,9, 59?66 (1971).
[42] V. V. Astrakhantsev, ?Pseudo-Riemannian symmetric spaces with commutative holonomy group,?Mat. Sb.,90, No. 2, 288?305 (1973).
[43] R. F. Bilyalov, ?Conformai transformation groups in gravitational fields,?Dokl. Akad. Nauk SSSR,152, No. 3, 570?572 (1963). · Zbl 0173.24202
[44] O. I. Bogoyavlenskii and S. P. Novikov, ?The qualitative theory of homogeneous cosmological models,?Tr. Seminara im. I. G. Petrovskogo, Moscow University, No. 1, 7?43 (1975).
[45] D. V. Volkov, D. P. Sorokin, and V. I. Tkach, ?Gauge fields in mechanisms of spontaneous compactification of subspaces,?Teor, i mat. fiz.,56, No. 2, 171?179 (1983). · Zbl 0572.53050
[46] N. V. Volkov, ?The local group of motions of ann-dimensional quasiorthogonal Riemannian spacetime? [in Russian],Leningrad Electrotechnical Institute (1979).
[47] E. I. Galyarskii, ?Two-dimensional groups of conformai symmetry and their generalizations,?Sovr. Vopr. Prikl. Mat. i Programmir. Mat. Nauki (Modern Questions of Applied Mathematics and Programming. Mathematical Sciences), Kishinev (1979), pp. 31?36.
[48] O. S. Germanov, ?On three-dimensional Riemannian spaces admitting a group of conformai transformations of order at most three? [in Russian]Gor’kii Polyt. Inst. (1986).
[49] V. P. Golubyatnikov and L. N. Pestov, ?On a group of conformai mappings ofR3 in stellar dynamics and the inverse kinematical problems of seismics,? in:Priblizhen. Metody Resheniya i Vopr. Korrektnosti Obratn. Zadach. (Approximate Methods of Solution and Questions of the Well-posedness of Inverse Problems), Novosibirsk (1981), pp. 35?43.
[50] I. V. Gribkov, ?On sufficient conditions for maximality of holonomy groups of Riemannian manifolds,?Vestn. MGU. Mat. Mekh., No. 3, 50?52 (1988). · Zbl 0651.53014
[51] N. A. Gromov, ?On passage to the limit in sets of groups of motions and the Lie algebras of spaces of constant curvature,?Mat. Zametki,32, No. 3, 355?364 (1982). · Zbl 0496.53007
[52] R. A. Daishev,Isometric Motions of an Ideal Fluid with a Massive Scalar Field [in Russian], Kazan University Press (1983).
[53] R. A. Daishev, ?Isometric motions of an ideal fluid with massive scalar field,?Gravitation and the Theory of Relativity [in Russian], Kazan Univ., No. 25, 40?57 (1988).
[54] B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko,Modern Geometry. Methods and Applications [in Russian], 2nd Ed., revised, Nauka, Moscow (1986).
[55] A. I. Egorov and L. I. Egorova, ?On some spaces that admit groups of motions of maximal order,?Liet. mat. rinkinys (Lithuanian Mathematical Collection),12, No. 2, 39?42 (1972).
[56] I. P. Egorov, ?Automorphisms in generalized spaces,?Itogi Nauki i Tekhniki, Ser. Probl. Geom.,10, 147?191 (1980).
[57] L. I. Zhukova, ?Riemannian spaces with projective group,?Uch. Zap. Penz. Fed. Inst.,124, 13?18 (1971).
[58] L. I. Zhukova, ?Projective mappings in Riemannian spaces (the isotropic case),?Uch. Zap. Penz. Ped. Inst.,124, 19?25 (1971).
[59] L. I. Zhukova, ?On groups of projective mappings of certain Riemannian spaces,?Uch. Zap. Penz. Ped. Inst,124, 26?30 (1971).
[60] L. I. Zhukova, ?Riemannian spaces admitting projective mappings,?Izv. Vuzov. Mat., No. 6, 37?41 (1973).
[61] G. G. Ivanov, ?Isometric motions in space-times with nonlinear scalar fields,?Izv. Vuzov. Mat., No. 2, 77?78 (1985). · Zbl 0574.53014
[62] G. G. Ivanov, ?On the immersion of space-time with isometric and conformai motions,?Izv. Vuzov. Mat., No. 1, 61?63 (1985).
[63] G. G. Ivanov and S. V. Chervon, ?Exact solutions in theSO(3)-invariant nonlinear sigma-model connected with isometric and homothetic symmetries,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 24, 37?44 (1987).
[64] V. R. Kaigorodov, ?Semisymmetric Lorentz spaces with perfect holonomy group,?Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 14?15, 113?120 (1978).
[65] N. R. Kamyshanskii, ?One-parameter groups of motions of pseudo-Riemannian spaces of dimension 2,?Tr. seminara po vektor. i tenzor. anal, s ikh pril. k geom., mekh., i fiz. (Proceedings of the seminar on vector and tensor analysis and their applications to geometry, mechanics, and physics), Moscow State University, No. 19, 218?239 (1979).
[66] N. R. Kamyshanskii, ?Classification of the complete simply connected subprojective pseudo-Riemannian spaces of V. F. Kagan,?Tr. seminara po vektor. i tenzor. anal, s ikh pril. k geom., mekh., i fiz. (Proceedings of the seminar on vector and tensor analysis and their applications to geometry, mechanics, and physics), Moscow State University, No. 20, 66?85 (1981).
[67] T. I. Kolesova, ?Decomposition of the isotropy group of some homogeneous Riemannian spaces,?Differential geometry and Lie algebras, Mosk. Obi. Ped. Inst. (Moscow Regional Pedagogical Institute), 66?70 (1983).
[68] M. T. Kondaurov, ?Motions and affine mappings in symmetric conformally Euclidean spaces? [in Russian], Publication of the JournalIzv. Vuzov. Matematika (1983).
[69] V. G. Kopp, ?On invariant groups of infinitesimal motions of a three-dimensional Lorentz space,?Tr. Geom. seminara Kazan. Univ., No. 17, 13?29 (1986). · Zbl 0627.53007
[70] N. S. Lipatov, ?Homothetic immobility in Gödel space,? in:Motions in Generalized Spaces [in Russian], Ryazan (1985), pp. 95?97.
[71] A. A. Lovkov, ?On a simply transitive group of homothetic mappings inV 4,?Uch. Zap. Penz. Ped. Inst.,124, 70?72 (1971).
[72] M. A. Malakhal’tsev, ?Free motions of the group of isometries on a space whose curvature is of constant sign. The group of isometries and the Ricci tensor? [in Russian], Kazan University (1986).
[73] V. E. Mel’nikov, ?On Riemannian spaces that admit a group of motions with decomposable isotropy group,?Izv. Vuzov. Mat., No. 2, 81?89 (1971).
[74] V. E. Mel’nikov, ?On groups of rotations of Riemannian spaces,? in:Proc. 27th Sci.-Tech. Conf. Mos. Inst. Radiotec., Electr., and Autom. [in Russian], Moscow (1978), pp. 53?60.
[75] J. Mikes, ?On concircular vector fields ?in the large? on compact Riemannian spaces? [in Russian], Odessa University (1988).
[76] J. Mikes, ?On the existence ofn-dimensional compact Riemannian spaces admitting nontrivial projective mappings ?in the large?,?Dokl. Akad. Nauk SSSR,305, No. 3, 534?536 (1989).
[77] J. Mikes and S. M. Pokas’,Lie groups of mappings of second order in associated Riemannian spaces [in Russian], Odessa University (1981).
[78] G. G. Mikhailichenko, ?Three-dimensional Lie algebras of mappings of a plane,?Sib. Mat. Zh.,23, No. 5, 132?141 (1982).
[79] N. V. Mitskevich and Yu. E. Senin, ?The topology and isometries of a De Sitter universe,?Dokl. Akad. Nauk SSSR,266, No. 3, 586?590 (1982). · Zbl 0516.53028
[80] I. M. Mitsnefes and I. A. Undalova, ?One-parameter groups of motions of the pseudo-Riemannian space V4,? in:Proc. of the 4th Sci. Conf. Young Scholars Mech./Math. Fac. [in Russian], Gor’kii (1979), pp. 64?71.
[81] D. O. Moldobaev, ?On the orders of the groups of conformai mappings in Riemannian spaces,? in:Studies in Integro-Differential Equations [in Russian], No. 16, 313?323 (1983). · Zbl 0587.53025
[82] D. O. Moldobaev, ?On conformally extended groups of motions of Riemannian spaces,? in:Studies in Topological and Generalized Spaces [in Russian], 63?70 (1988). · Zbl 0728.53017
[83] A. M. Mukhamedov, ?Maximally movable gravitational fields with respect to almost projective motions that preserve a quadratic geodesic complex,?Tr. Geom. Seminara Kazan. Univ., No. 11, 64?69 (1979).
[84] S. P. Novikov, ?Some problems of gravitational theory,?Usp. Mat. Nauk,28, No. 5, p. 266 (1973).
[85] S. Ya. Nus’, ?On infinitesimal isometries in the tangent bundle of the homethetically movable Riemannian spaceV 3 andV 4? [in Russian], Kazan University (1985).
[86] M. E. Osinovskii and O. A. Teslenko, ?Global analysis of vacuum spaces of third type admitting a twodimensional commutative group of isometries,?Gravitation and the Theory of Relativity [in Russian], Kazan Univ., No. 16, 111?119 (1980).
[87] V. I. Pan’zhenskii, ?On motions in a tangent bundle with the Sasaki metric,?Penz. Gos. Ped. Inst. (1989).
[88] A. Z. Petrov,New Methods in the General Theory of Relativity [in Russian], Nauka, Moscow (1966).
[89] S. M. Pokas’,Motions in Associated Riemannian Spaces [in Russian], Odessa University (1980).
[90] S. M. Pokas’,Infinitesimal Conformai Mappings in Associated Riemannian Spaces of Second Order [in Russian], Odessa University (1981).
[91] V. A. Popov, ?Extensibility of local isometry groups,?Mat. Sb.,135, No. 1, 12?13 (1988).
[92] K. Riives, ?Lie subgroups of motions of the Euclidean spaceR 5 and their orbits. II,?Tartu Ülikooli toimetised (Tartu University Reports), No. 342, 83?109 (1974). · Zbl 0342.53002
[93] N. R. Sibgatullin, ?On the theory of the neutron electrovacuum with Abelian group of motionsg 2 on V2,?Vestn. MGU. Mat.-Mekh., No. 2, 44?51 (1985).
[94] N. S. Sinyukov, ?Infinitesimal almost-geodesic mappings of affinely connected and Riemannian spaces. II,?Ukr. Geom. Sb., No. 11, 87?95 (1971).
[95] N. S. Sinyukov,Geodesic Mappings of Riemannian Spaces [in Russian], Nauka, Moscow (1979). · Zbl 0637.53020
[96] N. S. Sinyukov and S. M. Pokas’, ?Groups of motions of second degree in an associated Riemannian space,? in:Motions in Generalized Spaces [in Russian], Ryazan (1985), pp. 30?36.
[97] A. S. Solodovnikov, ?Projective mappings of Riemannian spaaces,?Usp. Mat. Nauk,11, No. 4, 45?116 (1956).
[98] A. E. Tralle, ?On the group of isometries of a generalized Riemannian symmetric space,?Mat. Zametki,41, No. 2, 248?256 (1987). · Zbl 0617.53052
[99] M. A. Ulanovskii, ?On conformai mappings of of the Lorentz metric,?Ukr. Geom. Sb., No. 27, 118?120 (1984).
[100] I. A. Undalova, ?Properly Riemannian spaces that admit a stationary-static group of motions,? Published byIzv. Vuzov. Mat., Kazan (1977).
[101] I. A. Undalova, ?One-parameter groups of motions with isotropic trajectories,? in:Differentsial’nye i Integral’nye Uravneniya, Gor’kii (1986), pp. 58?62.
[102] I. A. Undalova,One-parameter groups of projective mappings of a Riemannian space with isotropic trajectories [in Russian], Gor’kii University (1986).
[103] I. A. Undalova and S. N. Aryasova, ?A pseudo-Riemannian spaceV 4 admitting a one-parameter group of motions with an isolated fixed point? [in Russian], Gor’kii University (1987).
[104] I. A. Undalova and G. R. Eranova, ?One-parameter groups of homotheties of a Riemannian space,?Sb. St. Gor’kov. Univ. (Gor’kii Univ. Rpts.), No. 2, 105?109 (1975).
[105] I. A. Undalova and V. N. Markova, ?Properly Riemannian spaces admitting groups of motions of type B,?Proc. 8th Sci. Conf. Young Scholars Mech./Math. Fac. Gor’kii Univ., 25?26 April 1983, Part 1, Gor’kii University (1983), pp. 114?118.
[106] I. A. Undalova and L. Yu. Osipova, ?One-parameter groups of motions of type B of the Riemannian spacesV 3 andV 4,?Proc. 6th Sci. Conf. Young Scholars Mech./Math. Fac. Gor’kii Univ., Part 3, Gor’kii University (1981), pp. 392?400.
[107] I. A. Undalova and I. V. Tomarova, ?A Pseudo-Riemannian spaceV 4 that admits a Killing field with singularity? [in Russian], Gor’kii University (1988).
[108] A. S. Ferzaliev, ?On groups of motions in spaces with curvature tensor regarded as a cogredient function of a metric tensor and a skew-symmetric tensor,? in:Probl. Theory Grav. Elem. Part, [in Russian], Atomizdat, Moscow (1970), pp. 137?149.
[109] R. B. Chinak, ?On compact groups of isometries conjugate to a subgroup of the orthogonal group,?Sib. Mat. Zh.,28, No. 4, 207?209 (1987). · Zbl 0628.57022
[110] A. P. Chupakhin, ?Nonlinear conformally invariant equations in spacesV 4 with nontrivial conformai group,? in:Solid State Dynamics [in Russian], No. 25, 122?132 (1976).
[111] A. P. Chupakhin, ?Nontrivial conformai groups in Riemannian spaces,?Dokl. Akad. Nauk SSSR,246, No. 5, 1056?1058 (1979).
[112] Kh. Shadyev, ?On infinitesimal homotheties in the tangent bundle of a Riemannian manifold,?Izv. Vuzov. Mat., No. 9, 77?79 (1984). · Zbl 0572.53027
[113] Kh. Shadyev, ?On infinitesimal homotheties in the tangent bundle of a Riemannian manifold,? in:Probl. Multi-dim. Diff. Geom. and Appl. [in Russian], Samarkand (1988), pp. 12?26.
[114] I. G. Shandra, ?Infinitesimal homothetic mappings in the cotangent bundle,?Proc. Sci. Conf. Young Scholars Odessa Univ., May 16?17, 1985, Odessa University (1985), pp. 152?164.
[115] A. P. Shirokov, ?The geometry of tangent bundles and spaces over algebras,?Itogi Nauki i Tekhniki, Ser. Probl. Geom.,12, 61?95 (1980).
[116] P. I. Shushpanov, ?The group of motions of a spherical space and Lorentz transformations,?Nauch. Tr. Mosk. Inst. Nar. Khoz. (Proceedings of the Moscow Economics Institute), No. 96, 150?177 (1970).
[117] Noill H. Ackerman and C. C. Hsiung, ?Isometry of Riemannian manifolds to spheres. II,?Can. J. Math.,28, No. 1, 63?72 (1976). · Zbl 0333.53032 · doi:10.4153/CJM-1976-007-7
[118] Lynn L. Ackler and Chuan-Chih Hsiung, ?Isometry of Riemannian manifolds to spheres,?Ann. Math. Pura ed Appl,99, 53?64 (1974). · Zbl 0277.53023 · doi:10.1007/BF02413718
[119] Hassan Akbar-Zadeh and Raymond Couty, ?Espaces à tenseur de Ricci parallèle admettant des transformations projectives,?C. R. Acad. Sci.,284, No. 15, A891-A893 (1977). · Zbl 0345.53027
[120] Hassan Akbar-Zadeh and Raymond Couty, ?Espaces à tenseur de Ricci parallèle admettant des transformations projectives,?Rend. Math.,11, No. 1, 85?96 (1978). · Zbl 0393.53023
[121] Hassan Akbar-Zadeh and Raymond Couty, ?Transformations projectives de certaines variétés à connexion métrique,?C. R. Acad. Sci., Sér. 1,298, No. 7, 153?156 (1984). · Zbl 0568.53011
[122] Hassan Akbar-Zadeh and Raymond Couty, ?Transformations projectives des variétés munies d’une connexion métrique,?Ann. Math. Pura ed Appl, No. 148, 251?275 (1987). · Zbl 0636.53051 · doi:10.1007/BF01774292
[123] A. V. Aminova, ?The groups of symmetries in the spaces of general relativity,?Group-theoretic Methods in Mechanics. Proc. Int. Symp. Novosibirsk (1978), pp. 24?33.
[124] A. V. Aminova, ?On skew-orthonormal frame and parallel symmetric bilinear form on Riemannian manifolds,?Tensor,45, 1?13 (1987).
[125] A. V. Aminova, ?On geodesic mappings of Riemannian spaces,?Tensor,46, 179?186 (1987).
[126] Krishna Amur and S. S. Pujar, ?Isometry to spheres of Riemannian manifolds admitting a conformai transformation group,?J. Diff. Geom.,12, No. 2, 247?252 (1977). · Zbl 0421.53011 · doi:10.4310/jdg/1214433986
[127] Giuseppe Arcidiacono, ?A new projective relativity based on the De Sitter universe,?General Relativity and Gravitation,7, No. 11, 885?889 (1976). · doi:10.1007/BF00771020
[128] Abhay Ashtekar and Anne Magnon-Ashtekar, ?A technique for analyzing the structure of isometrics,?J. Math. Phys.,19, No. 7, 1567?1572 (1978). · Zbl 0443.53047 · doi:10.1063/1.523864
[129] Abhay Ashtekar and B. G. Schmidt, ?Null infinity and Killing fields,?J. Math. Phys.,21, No. 4, 862?867 (1980). · Zbl 0451.53047 · doi:10.1063/1.524467
[130] Abhay Ashtekar and Basilis C. Xanthopoulos, ?Isometries compatible with aysmptotic flatness at null infinity: a complete description,?J. Math. Phys.,19, No. 10, 2216?2222 (1978). · Zbl 0425.53036 · doi:10.1063/1.523556
[131] Daniel Asimov, ?Finite groups as isometry groups,?Trans. Amer. Math. Soc.,216, 389?391 (1976). · Zbl 0316.53039 · doi:10.2307/1997706
[132] L. Aulestia, L. Nuñez, A. Patiño, H. Rago, and L. Herrera, ?RadiatingC metric: an example of a proper Ricci collineation,?Nuovo dm.,B80, No. 1, 133?142 (1984).
[133] Christiane Barbance, ?Transformations conformes des variétés lorentziennes homogènes,?Tensor,39, Commem. Vol. 3, 173?178 (1982). · Zbl 0515.53045
[134] Christiane Barbance and Yvan Kerbrat, ?Sur les transformations conformes des variétés d’Einstein,?C. R. Acad. Sci.,AB286, No. 8, 391?394 (1978). · Zbl 0379.53026
[135] A. O. Barut, ?External (kinematical) and internal (dynamical) conformai symmetry and discrete mass spectrum,? in:Group Theory and Non-Linear Problems, Dordrecht, Boston (1974), pp. 249?259.
[136] André Batbedat, ?Sur la conjecture de A. Lichnerowicz,?Pubis. Dép. Math.,11, No. 3, 51?57 (1974).
[137] J. Becker, J. Harnad, M. Perroud, and P. Winternitz, ?Tensor fields invariant under subgroups of the conformai group of space-time,?J. Math. Phys.,19, No. 10, 2126?2153 (1978). · Zbl 0419.53013 · doi:10.1063/1.523571
[138] M. L. Bedran and B. Lesche, ?An example of affine collineation in the Robertson-Walker metric,?J. Math. Phys.,27, No. 9, 2360?2361 (1986). · Zbl 0601.53082 · doi:10.1063/1.527007
[139] J. K. Beem, P. E. Ehrlich, and S. Markvorsen, ?Timelike isometrics of space-times with nonnegative sectional curvature,? in:Topics in Differential Geometry: Colloq. Debrecen, 26 Aug.?1 Sept. 1984, Vol. 1, Amsterdam (1988), pp. 153?165.
[140] J. K. Beem, P. E. Ehrlich, and S. Markvorsen, ?Timelike isometries and Killing fields,?Geom. dedic.,26, No. 3, 247?258 (1988). · Zbl 0647.53045 · doi:10.1007/BF00183017
[141] Beverly K. Berger, ?Homothetic and conformai motions in spacelike slices of solutions of Einstein’s equations,?J. Math. Phys.,17, No. 7, 1268?1273 (1976). · doi:10.1063/1.523052
[142] David E. Blair, ?On the zeros of a conformai vector field,?Nagoya Math. J.,55, 1?3 (1974). · Zbl 0335.53038 · doi:10.1017/S0027763000016196
[143] Ashfaque H. Bokhari and Asghar Qadir, ?Symmetries of static, spherically symmetric space-times,?J. Math. Phys.,28, No. 5, 1019?1022 (1987). · Zbl 0618.53067 · doi:10.1063/1.527594
[144] C. Bona, ?Invariant conformai vectors in space-times admitting a groupG 3 of motions acting on spacelike orbitsS 2,?J. Math. Phys.,29, No. 11, 2462?2464 (1988). · Zbl 0668.53051 · doi:10.1063/1.528082
[145] Milo? Bo?ek, ?Existence of generalised symmetric Riemannian spaces with solvable isometry group,??as. pestov. mat.,105, No. 4, 368?384 (1980).
[146] C. P. Boyer and J. D. Finley III, ?Killing vectors in self-dual Euclidean Einstein spaces,?J. Math. Phys.,23, No. 6, 1126?1130 (1982). · Zbl 0484.53051 · doi:10.1063/1.525479
[147] Thomas P. Branson, ?Quasi-invariance of the Yang-Mills equations under conformai transformations and conformai vector fields,?J. Diff. Geom.,16, No. 2, 195?203 (1981). · Zbl 0509.53023 · doi:10.4310/jdg/1214436098
[148] Frederick Brickell and Kentaro Yano, ?Concurrent vector fields and Minkowski structures,?Kodai Math. Semin. Repts.,26, No. 1, 22?28 (1974). · Zbl 0307.53011 · doi:10.2996/kmj/1138846943
[149] A. J. Briginshaw, ?Causality and the group structure of space-time,?Int. J. Theor. Phys.,19, No. 5, 329?345 (1980). · Zbl 0447.53050 · doi:10.1007/BF00671987
[150] Marek Brodzki and Waclaw Sonelski, ?Zastosowanie pewnych podgrup grupy afinicznej zespolonej w geometrycznej teorii seci electrycznych,?Zesz. nauk. Psl., No. 593, 3?15 (1979).
[151] Jochen Brüning and Ernst Heintze, ?Représentations des groupes d’isométries dan les sous-espaces propres du laplacien,?C. R. Acad. Sci.,286, No. 20 A221-A223 (1978). · Zbl 0378.53020
[152] Robert L. Bryant, ?Metrics with holonomyG 2 or Spin(7),?Lect. Notes Math., No. 1111, 269?277 (1985). · doi:10.1007/BFb0084595
[153] Robert L. Bryant, ?Metrics with exceptional holonomy,?Ann. Math.,126, No. 3, 525?576 (1987). · Zbl 0637.53042 · doi:10.2307/1971360
[154] G. Burdet, J. Patera, M. Perrin, and P. Winternitz, ?The optical group and its subgroups,?J. Math. Phys.,19, No. 8, 1758?1780 (1978). · Zbl 0382.22010 · doi:10.1063/1.523875
[155] W. Byers, ?Isometry groups of manifolds of negative curvature,?Proc. Amer. Math. Soc.,54, 281?285 (1976). · Zbl 0321.53034 · doi:10.1090/S0002-9939-1976-0390960-6
[156] M. Cahen, ?A propos du groupe conforme de l’espace de Minkowski,?Bull. Cl. Sci. Acad. Roy. Belg.,62, No. 3, 199?206 (1976). · Zbl 0339.22016
[157] M. Cahen and Yvan Kerbrat, ?Transformations conformes des espaces symétriques pseudo-riemanniens,?C. R. Acad. Sci.,A285, No. 5,B285, No. 5, A383-A385 (1977). · Zbl 0364.53019
[158] M. Cahen and Yvan Kerbrat, ?Champs de vecteurs conformes et transformations conformes des espaces lorentziens symétriques,?J. math, pures et appl.,57, No. 2, 99?112 (1978). · Zbl 0386.53043
[159] M. Cahen and Yvan Kerbrat, ?Transformations conformes des espaces symétriques pseudo-riemanniens,?Ann. math, pura ed appl., No. 122, 257?289 (1982).
[160] Oscar A. Càmpoli, ?Clifford isometries of compact homogeneous Riemannian manifolds,?Rev. Union mat. argent.,31, No. 1?2, 44?49 (1983).
[161] Rongmei Cao, ?Space-times admitting a group of conformai motions generated by a time-like vector field,?J. Nanjing Univ.,5, No. 2, 249?253 (1988). · Zbl 0689.53042
[162] J. Carot and Li Mas, ?Conformai transformation and riseous fluids in general relativity,?J. Math. Phys.,27, No. 9, 2336?2339 (1986). · Zbl 0601.76138 · doi:10.1063/1.527004
[163] L. Castellani, R. D’Auria, P. Fré, and P. van Nieuwenhuizen, ?Holonomy groups, sesquidual torsion fields, andSU(8) ind=11 supergravity,?J. Math. Phys.,25, No. 11, 3209?3213 (1984). · Zbl 0557.53049 · doi:10.1063/1.526092
[164] Su-Shing Chen and Patrick Eberlein, ?Isometry groups of simply connected manifolds of nonpositive curvature,?Ill. J. Math.,24, No. 1, 73?103 (1980). · Zbl 0413.53029
[165] Cheng-Hsien Chep, ?On a Riemannian manifold admitting Killing vectors whose covariant derivatives are conformai Killing tensors,?Kodai Math. Semin. Repts.,23, No. 2, 168?171 (1971). · Zbl 0226.53006 · doi:10.2996/kmj/1138846317
[166] F. J. Chinea, ?Symmetries in tetrad theories,?Classical and Quantum Gravity,5, No. 1, 135?145 (1986). · doi:10.1088/0264-9381/5/1/018
[167] C. J. S. Clarke, ?The singular holonomy group,?Comm. Math. Phys.,58, No. 3, 291?297 (1978). · Zbl 0368.53035 · doi:10.1007/BF01614225
[168] H. I. Cohen, O. Leringe, and Y. Sundblad, ?The use of algebraic computing in general relativity,?Gen. Relat. and Gravit.,7, No. 3, 269?286, (1976). · doi:10.1007/BF00768528
[169] C. D. Collinson, ?Conservation laws in general relativity based upon the existence of preferred collineations,?Gen. Relat. and Gravit.,1, No. 2, 137?142 (1970). · Zbl 0331.53016 · doi:10.1007/BF00756893
[170] C. D. Collinson, ?Special subprojective motions in a Riemannian space,?Tensor,28, No. 2, 218?220 (1974).
[171] C. D. Collinson, ?Homothetic motions and the Hauser metric,?J. Math. Phys.,21, No. 1, 2601?2602 (1980). · doi:10.1063/1.524372
[172] C. D. Collinson, ?Proper affine collineations in Robertson-Walker space-times,?J. Math. Phys.,29, No. 9, 1972?1973 (1988). · Zbl 0669.53018 · doi:10.1063/1.527852
[173] C. D. Collinson and P. N. Smith, ?A comment on the symmetries of Kerr black holes,?Comm. Math. Phys.,56, No. 3, 277?279 (1977). · Zbl 0367.53009 · doi:10.1007/BF01614212
[174] Carlos Currás-Bosch, ?Killing vector fields and holonomy algebras,?Proc. Amer. Math. Soc.,90, No. 1, 97?102 (1984). · Zbl 0537.53046 · doi:10.2307/2044677
[175] Carlos Currás-Bosch, ?Killing vector fields and complex structures,?Lect. Notes Math., No. 1045, 36?42 (1984). · Zbl 0537.53046 · doi:10.1007/BFb0072163
[176] Carlos Currás-Bosch, ?Infinitesimal transformations on noncompact manifolds,?Ann. mat. pura ed appl., No. 149, 347?360 (1987). · Zbl 0637.53058 · doi:10.1007/BF01773942
[177] G. D’Ambra, ?Isometry groups of Lorentz manifolds,?Invent, math.,92, No. 3, 555?565 (1988). · Zbl 0647.53046 · doi:10.1007/BF01393747
[178] W. R. Davis and D. R. Oliver, Jr., ?Matter field space-times admitting mappings satisfying vanishing contraction of the Lie deformation of the Ricci tensor,?Ann. Inst. H. Poincaré,A28, No. 2, 197?206 (1978). · Zbl 0375.53010
[179] George Debney, ?Symmetry in Einstein-Maxwell space-time,?J. Math. Phys.,13, No. 10, 1469?1477 (1972). · doi:10.1063/1.1665865
[180] L. Defrise-Carter, ?Conformai groups and conformally equivalent isometry groups,?Comm. Math. Phys.,40, No. 3, 273?282 (1975). · Zbl 0322.53008 · doi:10.1007/BF01610003
[181] Ryszard Deszcz, ?Uwagi o kolineacjach rzutowych w pewnych klasach przestrzeni Riemanna,?Pr. nauk. Inst, matem. i fiz. teor. PWr., No. 8, 3?9 (1973).
[182] Ryszard Deszcz, ?On some Riemannian manifolds admitting a concircular vector field,?Demonstr. math.,9, No. 3, 487?495 (1976). · Zbl 0346.53009
[183] K. L. Duggal, ?Existence of two Killing vector fields on the space-time of general relativity,?Tensor,32, No. 3, 318?322 (1978).
[184] K. L. Duggal, ?Einstein-Maxwell equations compatible with certain Killing vectors with light velocity,?Ann. mat. pura ed appl,120, 263?264 (1979). · Zbl 0413.53024 · doi:10.1007/BF02411947
[185] K. L. Duggal and R. Sharma, ?Conformai collineations and anisotropic fluids in general relativity,?J. Math. Phys.,27, No. 10, 2511?2513 (1986). · Zbl 0618.76131 · doi:10.1063/1.527317
[186] C. C. Dyer and E. Honig, ?Geometry of homothetic Killing trajectories and stationary limit surfaces,?J. Math. Phys.,20, No. 1, 1?5 (1979). · Zbl 0415.53047 · doi:10.1063/1.523943
[187] Douglas M. Eardley, ?Self-similar space-times: geometry and dynamics,?Comm. Math. Phys.,37, No. 4, 287?309 (1974). · doi:10.1007/BF01645943
[188] Douglas M. Eardley, J. Isenberg, J. Marsden, and V. Moncrief, ?Homothetic and conformai symmetries of solutions of Einstein’s equations,?Comm. Math. Phys.,106, No. 1, 137?158 (1986). · Zbl 0604.53038 · doi:10.1007/BF01210929
[189] Patrick Eberlein, ?Isometry groups of simply connected manifolds of nonpositive curvature,?Acta, Math.,149, No. 1?2, 41?69 (1982). · Zbl 0511.53048 · doi:10.1007/BF02392349
[190] Paul E. Ehrlich, ?The displacement function of a timelike isometry,?Tensor,38, Comment. Vol. 2, 29?36 (1982). · Zbl 0503.53046
[191] Norio Ejiri, ?A negative answer to a conjecture of conformai transformations of Riemannian manifolds,?Tensor,33, No. 2, 261?266 (1981). · Zbl 0473.53036
[192] P. Enghis, ?Grupul de miscari al spatilorK 3*,?Stud. Univ. Babes-Bolydi Mat.,20, 16?20 (1975).
[193] P. Ernotte, ?Commutation properties of 2-parameter groups of isometrics,?J. Math. Phys.,21, No. 5, p. 954 (1980). · Zbl 0448.53043 · doi:10.1063/1.524523
[194] Frederick J. Ernst and Jerzy F. Pleba?ski, ?Killing structures and complex?-potentials,?Ann. Phys., (USA),107, No. 1?2, 266?282 (1977). · doi:10.1016/0003-4916(77)90212-3
[195] Abbas M. Faridi, ?Einstein-Maxwell equations and the conformai Ricci collineations,?J. Math. Phys.,28, No. 6, 1370?1376 (1987). · Zbl 0639.53072 · doi:10.1063/1.527540
[196] Jacqueline Ferrand, ?Sur un lemme d’Alekseevskii relatif aux transformations conformes,?C. R. Acad. Sci.,284, No. 2, A121-A123 (1977). · Zbl 0339.53028
[197] J. D. Finley III and J. F. Plebanski, ?Further heavenly metrics and their symmetries,?J. Math. Phys.,17, No. 4, 585?596 (1976). · doi:10.1063/1.522947
[198] J. D. Finley III and J. F. Pleba?ski, ?Killing vectors in planeH H space,?J. Math. Phys.,19, No. 4, 760?766 (1978). · Zbl 0395.53008 · doi:10.1063/1.523732
[199] J. D. Finley III and J. F. Plebanski, ?The classification of allH-spaces admitting a Killing vector,?J. Math. Phys.,20, No. 9, 1938?1945 (1979). · Zbl 0422.53025 · doi:10.1063/1.524294
[200] F. J. Flaherty, ?Champs de Killing sur des variétés Lorentziennes,?C. R. Acad. Sci.,280, No. 8, A517-A518 (1975). · Zbl 0301.53014
[201] G. Fubini, ?Sui gruppi trasformazioni geodetiche,?Mem. Accad. Sci. Torino, Cl. Fis. Mat. Nat.,53, No. 2, 261?313 (1903). · JFM 34.0658.03
[202] Masami Fujii, ?Some Riemannian manifolds admitting a concircular scalar field,?Math. J. Okayama Univ.,16, No. 1, 1?9 (1973). · Zbl 0272.53013
[203] David Garfinkle and Qingjun Tian, ?Space-times with cosmological constant and conformai Killing field have constant curvature,?Classical and Quantum Gravity,4, No. 1, 137?139 (1987). · Zbl 0614.53053 · doi:10.1088/0264-9381/4/1/016
[204] Andrzej Gebarowski, ?On conformai collineations in Riemannian spaces,?Pr. Nauk Inst. Matem, i Fiz. Teor., PWr., No. 8, 11?17 (1973). · Zbl 0263.53031
[205] E. Giodek, ?On Riemannian conformally symmetric spaces admitting projective collineations,?Colloq. Math.,26, 123?128 (1972).
[206] Carolyn S. Gordon and Edward N. Wilson, ?Isometry groups of Riemannian solvmanifolds,?Trans. Amer. Math. Soc.,307, No. 1, 245?269 (1988). · Zbl 0664.53022 · doi:10.1090/S0002-9947-1988-0936815-X
[207] Midori S. Goto, ?On isometry group of a manifold without focal points,?J. Math. Soc. Jap.,34, No. 4, 653?663 (1982). · Zbl 0499.53039 · doi:10.2969/jmsj/03440653
[208] Midori S. Goto and Morikuni Goto, ?Isometry groups of negatively pinched 3-manifolds,?Hiroshima Math. J.,9, No. 2, 313?319 (1979). · Zbl 0496.53029
[209] Alfred Gray, ?Weak holonomy groups,?Math. Z.,123, No. 4, 290?300 (1971). · Zbl 0222.53043 · doi:10.1007/BF01109983
[210] Robert E. Greene and Katsuhiro Shiohama, ?The isometry groups of manifolds admitting nonconstant convex functions,?J. Math. Soc. Japan,39, No. 1, 1?16 (1987). · Zbl 0611.53039 · doi:10.2969/jmsj/03910001
[211] W. Grycak, ?Null geodesic collineations in conformally recurrent manifolds,?Tensor,34, No. 3, 253?259 (1980). · Zbl 0448.53008
[212] W. Grycak, ?On affine collineations in conformally recurrent manifolds,?Tensor,35, No. 1, 45?50 (1981). · Zbl 0463.53007
[213] Xiaoying Guo, ?Riemannian manifolds admitting concircular vector fields,?J. Hangzhou Univ., Natur. Sci. Ed.,11, No. 2, 157?167 (1984). · Zbl 0544.53015
[214] William Dean Halford, ?Petrov typeN vacuum metrics and homothetic motions,?J. Math. Phys.,20, No. 6, 1115?1117 (1979). · doi:10.1063/1.524162
[215] William Dean Halford and R. P. Kerr, ?Einstein spaces and homothetic motions. I,?J. Math. Phys.,21, No. 1, 120?128 (1980). · Zbl 0452.53027 · doi:10.1063/1.524335
[216] G. S. Hall, ?Curvature collineations and the determination of the metric from the curvature in general relativity, ?Gen. Relat. and Gravit.,15, No. 6, 581?589 (1983). · Zbl 0514.53018 · doi:10.1007/BF00759572
[217] G. S. Hall, ?Curvature, metric and holonomy in general relativity,?Differ. Geom. and Appl., Proc. Conf. Brno, Aug. 24?30, 1986, pp. 127?136.
[218] G. S. Hall, ?Singularities and homothety groups in space-time,?Classical and Quantum Gravity,5, No. 5, L77-L80 (1988). · Zbl 0644.53062 · doi:10.1088/0264-9381/5/5/001
[219] G. S. Hall and J. Da Costa, ?Affine collineations in space-time,?J. Math. Phys.,29, No. 11, 2465?2472 (1988). · Zbl 0661.53017 · doi:10.1063/1.528083
[220] Leopold Halpern, ?Broken symmetry of Lie groups of transformations generating general relativistic theories of gravitation,?Int. J. Theor. Phys.,18, No. 11, 845?860 (1979). · Zbl 0444.53041 · doi:10.1007/BF00670462
[221] J. P. Harnad and R. B. Pettitt, ?Gauge theories for space-time symmetries. I,?J. Math. Phys.,17, No. 10, 1827?1837 (1976). · doi:10.1063/1.522829
[222] R. A. Harris and J. D. Zund, ?An investigation of Dubourdien’s list of space-times which admit holonomy groups,?J. Math. Phys.,19, No. 10, 2052?2054 (1978). · Zbl 0431.53060 · doi:10.1063/1.523583
[223] R. A. Harris and J. D. Zund, ?An investigation of the Kaigorodov space-times. I,?Tensor,36, No. 3, 233?241 (1982). · Zbl 0506.53011
[224] R. A. Harris and J. D. Zund, ?An investigation of the Kaigorodov space-times. II.?Tensor,36, No. 3, 242?248 (1982). · Zbl 0506.53012
[225] R. A. Harris and J. D. Zund, ?Continuous groups of the Kasner space-times,?Tensor,36, No. 3, 270?274 (1982). · Zbl 0503.53023
[226] R. A. Harris and J. D. Zund, ?An investigation of Kruchkovich’s homogeneous space-times,?Tensor,37, Commem. Vol. 1, 85?89 (1982). · Zbl 0485.53028
[227] R. A. Harris and J. D. Zund, ?Generalized Osinovsky space-times,?Tensor,40, No. 1, 49?53 (1983). · Zbl 0517.53030
[228] B. Kent Harrison and James L. Stevens, ?Using group theory to solve certain equations arising in general relativity,?Encyclia (formerlyProc. Utah Acad. Sci., Arts, and Lett.),55, 73?76 (1978).
[229] Peter Havas and Jerzy Plebanski, ?Conformai extensions of the Galilei group and their relation to the Schrödinger group,?J. Math. Phys.,19, No. 2, 482?493 (1978). · Zbl 0393.22016 · doi:10.1063/1.523670
[230] A. Held, ?Killing vectors in empty space algebraically special metrics. I,?Gen. Relat. and Gravit.,7, No. 2, 177?198 (1976). · Zbl 0349.53049 · doi:10.1007/BF00763434
[231] A. Held, ?Killing vectors in empty space algebraically special metrics. II,?J. Math. Phys.,17, No. 1, 39?45 (1976). · Zbl 0349.53049 · doi:10.1063/1.522778
[232] Marc Henneaux, ?Gravitational fields, spinor fields, and groups of motions,?Gen. Relat. and Gravit.,12, No. 2, 137?147 (1980). · Zbl 0442.53037 · doi:10.1007/BF00756468
[233] L. Herrera, J. Jiménez, L. Leal, J. Ponce de Leon, M. Esculpi, and V. Galina, ?Anisotropic fluids and conformai motions in general relativity,?J. Math. Phys.,25, No. 11, 3274?3278 (1984). · Zbl 0548.76113 · doi:10.1063/1.526075
[234] L. Herrera and J. Ponce de Leon, ?Perfect fluid spheres admitting a one-parameter group of conformai motions,?J. Math. Phys.,26, No. 4, 778?784 (1985). · doi:10.1063/1.526567
[235] Hitosi Hiramatu, ?On essentially isometric conformai transformation groups,?Kodai Math. Semin. Repts.,24, No. 2, 212?216 (1972). · Zbl 0237.53036 · doi:10.2996/kmj/1138846523
[236] Hitosi Hiramatu, ?On Riemannian manifolds admitting a one-parameter conformai transformation group,?Tensor,28, No. 1, 19?24 (1974). · Zbl 0294.53031
[237] Hitosi Hiramatu, ?On integral inequalities and their applications in Riemannian manifolds,?Geom. Dedic.,7, No. 3, 375?386 (1978). · Zbl 0382.53037 · doi:10.1007/BF00151534
[238] Hitosi Hiramatu, ?Integral inequalities and their applications in Riemannian manifolds admitting a projective vector field,?Geom. Dedic.,9, No. 4, 501?505 (1980). · Zbl 0449.53036 · doi:10.1007/BF00181565
[239] Chuan-Chih Hsiung and Louis W. Stern, ?Conformality and isometry of Riemannian manifolds to spheres,?Trans. Amer. Math. Soc.,163, 65?73 (1972). · doi:10.1090/S0002-9947-1972-0284948-4
[240] Heinz Huber, ?Über die Isometriegruppe einer kompakten Mannigfaltigkeit negativer Krümmung,?Helv. Phys. Acta,45, No. 2, 277?288 (1972).
[241] Z. Hussin and S. Sinzinkayo, ?Conformai symmetry and constants of motion,?J. Math. Phys.,26, No. 5, 1072?1076 (1985). · doi:10.1063/1.526540
[242] Ryosuke Ichida, ?On Riemannian manifolds of non-positive sectional curvature admitting a Killing vector field,?Math. J. Okayama Univ.,17, No. 2, 131?134 (1975). · Zbl 0321.53037
[243] Edwin Ihrig, ?The holonomy group in general relativity and the determination ofg ij from Ti j,?Gen. Relat. and Gravit.,7, No. 3, 313?323 (1976). · Zbl 0351.53041 · doi:10.1007/BF00768531
[244] Edwin Ihrig and D. K. Sen. ?Uniqueness of timelike Killing vector fields,?Ann. Inst. H. Poincaré,A23, No. 3, 297?301 (1975). · Zbl 0316.53047
[245] Hans-Christoph Im Hof, ?Über die Isometriegruppe bei kompakten Mannigfaltigkeiten negativer Krümmung,?Comm. Mat. Helv.,48, No. 1, 14?30 (1973). · Zbl 0258.53040 · doi:10.1007/BF02566108
[246] Edwin Ihrig and Ernst A. Ruh, ?Actions isométriques sur des variétés riemanniennes pincées,?C. R. Acad. Sci.,280, No. 13, A901-A904 (1975).
[247] Shigeru Ishihara and Mariko Konishi, ?Fibred Riemannian space with triple of Killing vectors,?Kodai Math. Semin. Repta.,25, No. 2, 175?189 (1973). · Zbl 0271.53047 · doi:10.2996/kmj/1138846770
[248] Mark Israelit, ?Bimetric Killing vectors and generation laws in bimetric theories of gravitation,?Gen. Relat. and Gravit,13, No. 6, 523?529 (1981). · Zbl 0467.53037 · doi:10.1007/BF00757238
[249] Minoru Isu, ?Notes on integral inequality for Riemannian manifolds admitting an infinitesimal conformai transformation,?Tensor,44, No. 3, 261?264 (1987). · Zbl 0675.53038
[250] Toshihiro Iwai, ?Liftings of infinitesimal transformations of a Riemannian manifold to its tangent bundle, with applications to dynamical systems,?Tensor,31, No. 1, 98?102 (1977). · Zbl 0353.53026
[251] Toshihiro Iwai, ?On infinitesimal affine and isometric transformations preserving respective vector fields,?Kodai Math. J.,1, No. 2, 171?186 (1978). · Zbl 0389.53019 · doi:10.2996/kmj/1138035537
[252] L. Kannenberg, ?Killing vectors in gauge supersymmetry,?J. Math. Phys.,19, No. 10, 2203?2206 (1978). · doi:10.1063/1.523554
[253] Adolf Karger, ?Geometry of the motion of robot manipulators,?Manuscr. Math.,62, No. 1, 115?126 (1988). · Zbl 0653.53007 · doi:10.1007/BF01258270
[254] Atsushi Katsuda, ?The isometry groups of compact manifolds wth negative Ricci curvature,?Proc. Amer. Math. Soc.,104, No. 2, 587?588 (1988). · Zbl 0693.53012 · doi:10.1090/S0002-9939-1988-0962832-5
[255] Gerald H. Katzin and Jack Levine, ?Charge conservation as concomitant of conformai motions coupled to generalized gauge transformations,?J. Math. Phys.,21, No. 4, 902?908 (1980). · Zbl 0449.70018 · doi:10.1063/1.524475
[256] Louis H. Kauffman, ?Transformations in special relativity,?Int. J. Theor. Phys.,24, No. 3, 223?236 (1985). · Zbl 0567.22017 · doi:10.1007/BF00669788
[257] Yvan Kerbrat, ?Existence d’homothéties infinitésimales sur une variété munie d’une connexion linéaire symétrique complète,?C. R. Acad. Sci.,280, No. 9, A587-A589 (1975). · Zbl 0297.53018
[258] Yvan Kerbrat, ?Transformations conformes des variétés pseudoriemanniennes,?J. Diff. Geom.,11, No. 4, 547?571 (1976). · Zbl 0356.53019 · doi:10.4310/jdg/1214433724
[259] R. P. Kerr and G. C. Debney, Jr., ?Einstein spaces with symmetry groups,?J. Math. Phys.,11, No. 9, 2807?2817 (1970). · Zbl 0209.53501 · doi:10.1063/1.1665451
[260] Paul Kersten and Martin Ruud, ?The harmonic map and Killing fields for self-dualSU(3) Yang-Mills equations,?J. Phys. A: Math, and Gen.,17, No. 5, L227-L230 (1984). · Zbl 0539.58006 · doi:10.1088/0305-4470/17/5/001
[261] Andrzej Kieres, ?A pseudo-group of motions of a certain pseudo-Riemannian space,?Ann. UMCS,A34, 65?71 (1980). · Zbl 0566.57026
[262] In-Bae Kim, ?Special concircular vector fields in Riemannian manifolds,?Hiroshima Math. J.,13, No. 1, 77?91 (1982). · Zbl 0482.53029
[263] Shin-ichi Kitamura, ?The groups of motions of some stationary axially symmetric space-times,?Tensor,35, No. 2, 183?186 (1981). · Zbl 0471.53046
[264] Shoshichi Kobayashi, ?Transformation groups in differential geometry,?Ergeb, der Math. und ihrer Grenzgeb., No. 70, Springer, Berlin (1972).
[265] Shoshichi Kobayashi, ?Projective invariant metrics for Einstein spaces,?Nagoya Math. J.,73, 171?174 (1979). · Zbl 0413.53030 · doi:10.1017/S0027763000018389
[266] Shoshichi Kobayashi and Katsumi Nomizu,Foundations of Differential Geometry, Vols. 1?2, Interscience, New York (1963?1969). · Zbl 0091.34802
[267] Hidemaro Kôjyô, ?On conformai Killing tensors of a Riemannian manifold of constant curvature,?Hokkaido Math. J.,2, No. 2, 236?242 (1973). · Zbl 0281.53014 · doi:10.14492/hokmj/1381758984
[268] Charalampos A. Kolassis, ?On the effect of space-time isometries on the neutrino fields,?J. Math. Phys.,23, No. 9, 1630?1638 (1982). · Zbl 0688.53036 · doi:10.1063/1.525547
[269] Czes?aw Konopka, ?On some transformations in separately Einstein spaces,?Pr. Nauk Inst. Mat. i Fiz. Teor. PWr., No. 8, 25?32 (1973).
[270] Oldrich Kowalski, ?Free periodic isometries of Riemannian manifolds,?J. London Math. Soc.,20, No. 2, 334?338 (1979). · Zbl 0407.53010 · doi:10.1112/jlms/s2-20.2.334
[271] Tsunehira Koyanagi, ?On a certain property of a Riemannian space admitting a special concircular scalar field,?J. Fac. Sci. Hokkaido Univ., Ser. I,22, No. 3?4, 154?157 (1972). · Zbl 0241.53028
[272] J. P. Krisch, ?On the Killing surface-event horizon relation,?J. Math. Phys.,22, No. 4, 663?666 (1981). · Zbl 0483.70001 · doi:10.1063/1.524973
[273] Martin Légaré, ?Symmetry reduction and simple supersymmetric models,?J. Math. Phys.,28, No. 4, 935?939 (1987). · Zbl 0612.58051 · doi:10.1063/1.527584
[274] Jack Levine, ?Curvature collineations in Riemannian spaces admittingr fields of parallel vectors,?Tensor,24, 389?392 (1972). · Zbl 0257.53025
[275] Andre Lichnerowicz,Geometry of Groups of Transformations, Leyden (1977). · Zbl 0348.53001
[276] Mu-Chou Liu, ?Local holonomy groups of induced connections,?Proc. Amer. Math. Soc.,42, No. 1, 272?278 (1974). · Zbl 0277.53011 · doi:10.1090/S0002-9939-1974-0331266-9
[277] J. F. Torres Lopera, ?Geodesies and conformai transformations of Heisenberg-Reiter spaces,?Trans. Amer. Math. Soc.,306, No. 2, 489?498 (1988). · Zbl 0651.53036 · doi:10.2307/2000808
[278] Eric A. Lord, ?Geometrical interpretation of Inönü-Wigner contractions,?Int. J. Theor. Phys.,24, No. 7, 723?730 (1985). · doi:10.1007/BF00670879
[279] Eric A. Lord, ?Gauge theory of a group of diffeomorphisms. II. The conformai and de Sitter groups,?J. Math. Phys.,27, No. 12, 3051?3054 (1986). · Zbl 0616.53061 · doi:10.1063/1.527234
[280] Eric A. Lord and P. Goswami, ?Gauge theory of a group of diffeomorphisms. I. General principles,?J. Math. Phys.,27, No. 9, 2415?2422 (1986). · Zbl 0602.53067 · doi:10.1063/1.526980
[281] B. Lukács, Z. Perjés, and A. Sebestyén, ?Null Killing vectors,?J. Math. Phys.,22, No. 6, 1248?1253 (1981). · doi:10.1063/1.525049
[282] Gordon W. Lukesh, ?Compact transitive isometry groups,?London Math. Soc. Lect. Note Ser., No. 26, 301?304 (1977). · Zbl 0353.53029
[283] Gordon W. Lukesh, ?Isometry groups acting with one orbit type,?Geom. Dedic.,12, No. 4, 347?350 (1982). · Zbl 0487.53032 · doi:10.1007/BF00147576
[284] Walter C. Lynge, ?Zero points of Killing vector fields, geodesic orbits, curvature, and cut locus,?Trans. Amer. Math. Soc.,172, 501?506 (1972). · Zbl 0223.53035 · doi:10.1090/S0002-9947-1972-0355899-1
[285] Walter C. Lynge, ?Sufficient conditions for periodicity of a Killing vector field,?Proc. Amer. Math. Soc.,38, No. 3, 614?616 (1973). · Zbl 0236.53041 · doi:10.1090/S0002-9939-1973-0317230-3
[286] R. Maartens, ?Affine collineations in Robertson-Walker space-time.?J. Math. Phys.,28, No. 9, 2051?2052 (1987). · Zbl 0635.53014 · doi:10.1063/1.527414
[287] R. Maartens, D. P. Mason, and M. Tsamparlis, ?Kinematic and dynamic properties of conformai Killing vectors in anisotropic fluids,?J. Math. Phys.,27, No. 12, 2987?2994 (1986). · Zbl 0609.53031 · doi:10.1063/1.527225
[288] Malcolm MacCallum, ?The mathematics of anisotropic spatially-homogeneous cosmologies. Physics of the Expanding Universe. Cracow School of Cosmology. Jodlowy Dwor, Sept., 1978,Lect. Notes Phys.,109, 1?59 (1979). · doi:10.1007/3-540-09562-4_1
[289] Masao Maeda, ?The isometry groups of compact manifolds with non-positive curvature,?Proc. Jap. Acad.,51, Suppl, 790?794 (1975). · Zbl 0341.53026 · doi:10.3792/pja/1195518435
[290] M. D. Maia, ?Combined symmetries in curved space-times,?J. Math. Phys.,25, No. 6, 2090?2094 (1984). · Zbl 0553.53046 · doi:10.1063/1.526365
[291] L. N. Mann, ?Gaps in the dimensions of isometry groups of Riemannian manifolds,?J. Diff. Geom.,11, No. 2, 293?298 (1976). · Zbl 0332.53031 · doi:10.4310/jdg/1214433426
[292] Freydoon Mansouri and Louis Witten, ?Isometries and dimensional reduction,?J. Math. Phys.,25, No. 6, 1991?1994 (1984). · Zbl 0548.53026 · doi:10.1063/1.526392
[293] Y. B. Maralabhavi, ?A note on the conformai transformation in a W-recurrent space,?Indian J. Pure and Appl. Math.,16, No. 4, 365?372 (1985). · Zbl 0568.53014
[294] Stefano Marchiafava, ?Alcune osservazioni riguardanti i gruppi di LieG 2 e Spin(7), candidati a gruppi di olonomia,?Ann. Mat. Pura ed Appl,129, 247?264 (1981). · Zbl 0483.53018 · doi:10.1007/BF01762145
[295] Stefano Marchiafava, ?Characterization of Riemannian manifolds with weak holonomy group G2 (following A. Gray),?Math. Z.,178, No. 2, 157?162 (1981). · Zbl 0449.53026 · doi:10.1007/BF01262037
[296] George M?rgulescu, ?Equations invariantes par rapport au groupe conforme affine,?Rev. Raum. Math. Pures et Appl,19, No. 2, 209?212 (1974).
[297] George M?rgulescu, ?Les représentations spinorielles du groupe conforme de l’espace de Minkowski,? in:Lucr. Coloc. Nat. Geom. si Topol, Busteni, 27?30 iun., 1981, Bucuresti (1983), pp. 226?233.
[298] Jésus Martin, ?Etude de certains groupes d’isométries agissants sur la variété espace-temps,?C. R. Acad. Sci.,271, No. 20, A1036-A1038 (1970).
[299] E. Martinez and J. L. Sanz, ?Space-times with intrinsic symmetries on the three-spacest= constant,?J. Math. Phys.,26, No. 4, 785?791 (1985). · doi:10.1063/1.526568
[300] Hiroo Matsuda, ?On n-dimensional Lorentz manifolds admitting an isometry group of dimensionn(n-l)/2 + 1 forn ? 4,?Hokkaido Math. J.,15, No. 2, 309?315 (1986). · Zbl 0608.53057 · doi:10.14492/hokmj/1381518228
[301] Hiroo Matsuda, ?Onn-dimensional Lorentz manifolds admitting an isometry group of dimension n(n-l)/2 + 1,?Proc. Amer. Math. Soc.,100, No. 2, 329?334 (1987). · Zbl 0621.53049
[302] J. Dermott McCrea, ?Poincaré gauge theory of gravitation: foundations, exact solutions, and computer algebra,?Led. Notes Math., No. 1251, 222?237 (1987). · doi:10.1007/BFb0077323
[303] D. P. Mason and R. Maartens, ?Kinematics and dynamics of conformai collineations in relativity,?J. Math. Phys.,28, No. 9, 2182?2186 (1987). · Zbl 0635.76132 · doi:10.1063/1.527431
[304] D. P. Mason and M. Tsamparlis, ?Spacelike conformai Killing vectors and spacelike congruences,?J. Math. Phys.,26, No. 11, 2881?2901 (1985). · Zbl 0587.53062 · doi:10.1063/1.526714
[305] C. B. G. McIntosh, ?Homothetic motions in general relativity,?Gen. Relat. and Gravit.,7, No. 2, 199?213 (1976). · doi:10.1007/BF00763435
[306] C. B. G. McIntosh, ?Homothetic motions with null homothetic bivectors in general relativity,?Gen. Relat. and Gravit.,7, No. 2, 215?218 (1976). · doi:10.1007/BF00763436
[307] C. B. G. McIntosh, ?Symmetries and exact solutions of Einstein’s equations. Gravitational Radiation, Collapsed Objects, and Exact Solutions. Proc. Einstein Cent. Summer School, Perth, Jan. 1979,?Led. Notes Phys., No. 125, 469?476 (1980). · doi:10.1007/3-540-09992-1_119
[308] C. B. G. McIntosh and W. D. Haiford, ?The Riemann tensor, the metric tensor, and curvature collineations in general relativity,?J. Math. Phys.,23, No. 3, 436?441 (1982). · Zbl 0491.53018 · doi:10.1063/1.525366
[309] M. B. Mensky, ?Group of parallel transports and description of particles in curved space-time,?Lett. Math. Phys.,2, No. 3, 175?180 (1978). · doi:10.1007/BF00406402
[310] Kam-Ping Mok, ?On the differential geometry of frame bundles of Riemannian manifolds,?J. reine und angew. Math.,302, 16?31 (1978). · Zbl 0378.53016
[311] Vincent Moncrief, ?Space-time symmetries and linearization stability of the Einstein equations,?J. Math. Phys.,17, No. 10, 1893?1902 (1976). · Zbl 0314.53035 · doi:10.1063/1.522814
[312] Osvaldo M. Moreschi and George A. J. Sparling, ?On Riemannian spaces with conformai symmetries, or a tool for the study of generalized Kaluza-Klein theories,?J. Math. Phys.,24, No. 2, 303?310 (1983). · Zbl 0508.53065 · doi:10.1063/1.525680
[313] Gaetano Moschetti, ?Homothetic solutions of Einstein’s equations and shock waves,?J. Math. Phys.,22, No. 4, 830?834 (1981). · Zbl 0515.76130 · doi:10.1063/1.524947
[314] Tadashi Nagano and Takushiro Ochiai, ?On compact Riemannian manifolds admitting essential projective transformations,?J. Fac. Sci. Univ. Tokyo, Sec. 1A,33, No. 2, 233?246 (1986). · Zbl 0645.53022
[315] J. Navez, ?The groups of motions of space-times admitting a parallel null vector field,?Bull. Soc. Roy. Sci. Liège,41, No. 9?10, 484?502 (1972). · Zbl 0265.53023
[316] N. I. Nedit?, ?On space-times with Killing pairing,?Bull. Math. Soc. Sei. Math. RSR,22, No. 2, 175?182 (1978).
[317] Y. Ne’eman and T. N. Sherry, ?Affine extensions of supersymmetry: The finite case,?Nucl. Phys.,B138, No. 1, 31?44 (1978). · doi:10.1016/0550-3213(78)90155-4
[318] L. K. Norris and W. R. Davis, ?Infinitesimal holonomy group, structure and geometrization,?Ann. Inst. H. Poincaré,A31, No. 4, 387?398 (1979). · Zbl 0432.53054
[319] Morio Obata, ?The conjectures on conformai transformations of Riemannian manifolds,?J. Diff. Geom.,6, No. 2, 247?258 (1971). · Zbl 0236.53042 · doi:10.4310/jdg/1214430407
[320] Takushiro Ochiai and Tsunero Takahashi, ?The group of isometries of a left-invariant Riemannian metric on a Lie group,?Math. Ann.,223, No. 1, 91?96 (1976). · Zbl 0318.53042 · doi:10.1007/BF01360280
[321] Dan I. Papuc and Ion P. Popescu, ?Remarques sur les actions des groupes projectifs et affines sur leurs algèbres de Lie,?C. R. Acad. Sci.,A279, No. 14, 565?567 (1974). · Zbl 0294.22013
[322] Matilde Pascua, ?Una soluzione delle equazioni di Einstein-Maxwell ammettente un gruppoG 7 di automorfismi,?Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat., e Natur.,59, No. 1?2, 91?99 (1975).
[323] Eliano Pessa, ?A new unified field theory based on the conformai group,?Gen. Relat. and Gravit.,12, No. 10, 857?862 (1980). · Zbl 0453.53023 · doi:10.1007/BF00763060
[324] Pierre Pigeaud and Moussa Sakoto, ?Transformations infinitésimales conformes fermées des variétés riemanniennes,?C. R. Acad. Sci.,274, No. 19, A1406-A1408 (1972). · Zbl 0241.53018
[325] Jean-François Pommaret, ?Thermodynamique et théorie des groupes,?C. R. Acad. Sci., Ser. 1,307, No. 16, 839?842 (1988).
[326] G. Prasad, ?Relativistic electromagnetic fluids and Ricci collineations,?Indian J. Pure and Appl. Math.,10, No. 1, 94?99 (1979). · Zbl 0395.76097
[327] Asghar Qadir and M. Ziad, ?Static spherically symmetric space-times with six Killing vectors,?J. Math. Phys.,29, No. 11, 2473?2474 (1988). · Zbl 0668.53050 · doi:10.1063/1.528084
[328] Pham Mau Quan, ?Sur les transformations qui laissent invariantes les équations d’Einstein,?C. R. Acad. Sci.,285, 1081?1084 (1977). · Zbl 0376.53015
[329] Shri Ram and H. S. Pandey, ?Curvature collineations in a certain cosmological space-time,?Indian J. Pure and Appl. Math.,13, No. 10, 1200?1203 (1982). · Zbl 0502.53018
[330] M. J. Reboucas and J. E. Aman, ?Computer-aided study of a class of Riemannian space-times,?J. Math. Phys.,28, No. 4, 888?892 (1987). · Zbl 0615.53067 · doi:10.1063/1.527578
[331] W. Roter, ?Some remarks on infinitesimal conformai motions in conformally symmetric manifolds,?Tensor,36, No. 1, 8?10 (1981). · Zbl 0477.53024
[332] Moussa Sakoto, ?Transformations infinitésimales conformes d’une variété riemannienne quotient,?C. R. Acad. Sci.,272, No. 21, A1407-A1409 (1971). · Zbl 0215.23201
[333] Eliane Salem, ?Une généralisation du théorème de Mayers-Steenrod aux pseudo-groupes d’isométries,?Ann. Inst. Fourier,38, No. 1, 185?200 (1988). · Zbl 0613.58041 · doi:10.5802/aif.1139
[334] Bartolo Sanno, ?Sulle superficie che si corrispondono per transformazione di Lie e su un formulario completo tra gli invarianti del gruppo conforme e gli invarianti del gruppo proiettivo,?Rend. Circ. Math. Palermo,24, No. 1?2, 168?176 (1975). · Zbl 0352.53003 · doi:10.1007/BF02849251
[335] B. G. Schmidt, ?Homogeneous Riemannian spaces and Lie algebras of Killing fields,?Gen. Relat. and Gravit.,2, No. 2, 105?120 (1971). · Zbl 0333.53035 · doi:10.1007/BF02450443
[336] Victor Schroeder, ?Tits metric and the action of isometries at infinity,? in:Manifolds of Positive Curvature, Boston (1985), pp. 212?220.
[337] Matthias Schubert, ?Die Geometrie nilpotenter Liegruppen mit linksinvarianter Metrik,?Bonn. Math. Schr., No. 149 (1983).
[338] Ramesh Sharma, ?A relation between an affine Killing vector and the strain tensor of a pseudo-Riemannian manifold,?Math. Repts. Acad. Sci. Can.,4, No. 5, 305?307 (1982). · Zbl 0492.53015
[339] Ramesh Sharma, ?Proper conformai symmetries of conformai symmetric space-times,?J. Math. Phys.,29, No. 11, 2421?2422 (1988). · Zbl 0659.53029 · doi:10.1063/1.528127
[340] Ramesh Sharma and K. L. Duggal, ?Characterization of an affine conformai vector field,?Math. Repts. Acad. Sci. Can.,7, No. 3, 201?205 (1985).
[341] D. J. Shetty, ?On harmonic and Killing vector fields in a submanifold,?Indian J. Pure and Appl. Math.,11, No. 8, 983?987 (1980). · Zbl 0451.53044
[342] Richard F. Sigal, ?A note on proper homothetic motions,?Gen. Relat. and Gravit.,5, No. 6, 737?739 (1974). · Zbl 0335.53052 · doi:10.1007/BF00761929
[343] S. T. C. Siklos, ?Some Einstein spaces and their global properties,?J. Phys. A: Math, and Gen.,14, No. 2, 395?409 (1981). · doi:10.1088/0305-4470/14/2/016
[344] K. P. Singh and D. N. Sharma, ?Ricci and Maxwell collineations in a null electromagnetic field,?J. Phys. A: Math, and Gen.,8, No. 12, 1875?1881 (1975). · doi:10.1088/0305-4470/8/12/005
[345] K. P. Singh and Shri Ram, ?Curvature collineation for plane symmetric cosmological model,?Indain J. Pure and Appl. Math.,5, No. 3, 241?245 (1974).
[346] S. Sinzinkayo and J. Demaret, ?On solutions of Einstein and Einstein-Yang-Mills equations with (maximal) conformai subsymmetries,?Gen. Relat. and Gravit.,17, No. 2, 187?201 (1985). · Zbl 0561.53069 · doi:10.1007/BF00760531
[347] Dumitru Smaranda, ?On the Riemann space with intransitive group of motions,?Tensor,28, No. 3, 273?274 (1974). · Zbl 0318.53047
[348] P. K. Smrz, ?Relativity and deformed Lie groups,?J. Math. Phys.,19, No. 10, 2085?2088 (1978). · Zbl 0422.53028 · doi:10.1063/1.523563
[349] P. K. Smrz, ?A gauge field theory of spacetime based on the de Sitter group,?Found. Phys.,10, No. 3?4, 267?280 (1980). · doi:10.1007/BF00715072
[350] G. E. Sobczyk, ?Killing vectors and embedding of exact solutions in general relativity,? in:Clifford Algebras and Appl. Math. Phys.: Proc. NATO and SERC Workshop, Canterbury, 15?27 Sept., 1985, Dordrecht (1986), pp. 227?244.
[351] F. Söler and G. Séguin, ?Groupe d’isométries de S2, S2 xR, S 3, etSi3 x R,?Tensor,36, No. 3, 249?255 (1982).
[352] P. Stavre, ?Asupra unor cîmpuri de vectori,?Stud, si cerc, mat.,26, No. 2, 281?287 (1974).
[353] Ann K. Stehney and Richard S. Millman, ?Riemannian manifolds with many Killing vector fields,?Fund. Math.,105, No. 3, 241?247 (1980). · Zbl 0453.53040
[354] Kunio Sugahara, ?The isometry group and the diameter of a Riemannian manifold with positive curvature,?Math. Jap.,27, No. 5, 631?634 (1982). · Zbl 0497.53048
[355] T. Suguri and S. Ueno, ?Some notes on infinitesimal conformai transformations,?Tensor,24, 253?260 (1972). · Zbl 0251.53015
[356] Yoshihiko Suyama, ?Riemannian manifolds admitting commutative Killing vector fields,?Math. J. Okayama Univ.,26, 199?218 (1984). · Zbl 0571.53029
[357] Yoshihiko Suyama and Yotaro Tsukamoto, ?Riemannian manifolds admitting a certain conformal transformation group,?J. Diff. Geom.,5, No. 3?4, 415?426 (1971). · Zbl 0223.53042 · doi:10.4310/jdg/1214430004
[358] Alois Svec, ?Finite Killing vector fields,?Comment. Math. Univ. Carol,18, No. 1, 65?69 (1977).
[359] L. B. Szabados, ?Commutation properties of cyclic and null Killing symmetries,?J. Math. Phys.,28, No. 11, 2688?2691 (1987). · Zbl 0642.53028 · doi:10.1063/1.527712
[360] D. A. Szafron, ?Intrinsic isometry groups in general relativity,?J. Math. Phys.,22, No. 3, 543?548 (1981). · Zbl 0454.53039 · doi:10.1063/1.524923
[361] J. Szenthe, ?Sur les sous-groupes d’isotropie d’actions isométriques sur les variétés riemanniennes à courbure positive,?Stud. Sci. Math. Hung.,15, No. 1?3, 89?92 (1980). · Zbl 0511.53047
[362] J. Szenthe, ?A generalization of the Weyl group,?Acta Math. Hung.,41, No. 3?4, 347?357 (1983). · Zbl 0545.57014 · doi:10.1007/BF01961321
[363] Shun-ichi Tachibana, ?On the geodesic projective transformation in Riemannian spaces,?Hokkaido Math. J.,1, No. 1, 87?94 (1972). · Zbl 0246.53047 · doi:10.14492/hokmj/1381759040
[364] Shun-ichi Tachibana, ?On examples of Riemannian spaces harmonic relative to Killing vectors,?Natur. Sci. Rept. Ochanomizu Univ.,23, No. 1, 1?7, (1972). · Zbl 0265.53015
[365] Shun-ichi Tachibana, ?On Riemannian spaces admitting geodesic conformai transformations,?Tensor,25, 323?331, (1972). · Zbl 0233.53008
[366] Hitoshi Takagi, ?Conformally flat Riemannian manifolds admitting a transitive group of isometries,?Tôhoku Math. J.,27, No. 1, 103?110 (1975). · Zbl 0311.53062 · doi:10.2748/tmj/1178241040
[367] Kwoichi Tandai, ?Riemannian manifold admitting more thann?1 linearly independent solutions of ?2?t+ c2?g=0,?Hokkaido Math. J.,1, No. 1, 12?15 (1972). · Zbl 0252.53016 · doi:10.14492/hokmj/1381759031
[368] N. Tariq and B. 0. J. Tupper, ?Curvature collineations in Einstein-Maxwell space-times and in Einstein spaces,?Tensor,31, No. 1, 42?48 (1977). · Zbl 0355.53011
[369] G. F. Torres del Castillo, ?Killing vectors in algebraically special space-times,?J. Math. Phys.,25, No. 6, 1980?1984 (1984). · Zbl 0548.53030 · doi:10.1063/1.526390
[370] R. W. Tucker, ?Affine transformations and the geometry of superspace,?J. Math. Phys.,22, No. 2, 422?429 (1981). · Zbl 0457.58021 · doi:10.1063/1.524908
[371] Constantin Udriste, ?Proprietati ale cîmpurilor vectoriale afine si proiective,?Stud, si Cerc. Mat.,36, No. 5, 444?452 (1984).
[372] Constantin Udriste, ?Cîmpuri vectoriale conforme pe varietati Riemann ou tensorul Rirri negativ semidefinit,? in:Lucr. Conf. Nat. Geom. si Topol., Tîrgoviste, 12?14 Apr., 1986, Bucuresti (1988), pp. 311?314.
[373] Bernard Vignon, ?Sur les vecteurs conformes fermés d’une variété pseudo-riemannienne,?C. R. Acad. Sci.,276, No. 26, A1689-A1691 (1973). · Zbl 0258.53045
[374] Gheorghe Vr?nceanu, ?Sur les groupes d’holonomie des espacesV n plongés dansE n+p sans torsion,?Rev. Roum. Math. Pures et Appl.,19, No. 1, 125?128 (1974).
[375] J. Wainwright and P. A. E. Yaremovicz, ?Killing vector fields and the Einstein-Maxwell field equations with perfect fluid source,?Gen. Relat. and Gravit.,7, No. 4, 345?359 (1976). · Zbl 0365.76098 · doi:10.1007/BF00763408
[376] J. Wainwright and P. A. E. Yaremovicz, ?Symmetries and the Einstein-Maxwell field equations. The null field case,?Gen. Relat. and Gravit.,7, No. 7, 593?608 (1976). · Zbl 0365.76099 · doi:10.1007/BF00763408
[377] Edward N. Wilson, ?Isometry groups on homogeneous nilmanifolds,?Geom. Dedic.,12, No. 3, 337?346 (1982). · Zbl 0489.53045 · doi:10.1007/BF00147318
[378] M. L. Wooley, ?On Killing vectors and invariance transformations of the Einstein-Maxwell equations,?Math. Proc. Cambridge Phil. Soc.,80, No. 2, 357?364 (1976). · Zbl 0336.53021 · doi:10.1017/S0305004100052981
[379] Toshikiyo Yamada, ?On conharmonic and concircular transformations,?J. Asahikawa Techn. Coll., No. 16, 163?170 (1979). · Zbl 0404.53021
[380] Takao Yamaguchi, ?The isometry groups of Riemannian manifolds admitting strictly convex functions,?Ann. Sci. ec. Norm. Sup.,15, No. 1, 205?212 (1982). · Zbl 0501.53028 · doi:10.24033/asens.1425
[381] Takao Yamaguchi, ?The isometry groups of manifolds of nonpositive curvature with finite volume,?Math. Z.,189, No. 2, 185?192 (1985). · Zbl 0554.53029 · doi:10.1007/BF01175043
[382] Kazunari Yamauchi, ?On infinitesimal projective transformations,?Hokkaido Math. J.,3, No. 2, 262?270 (1974). · Zbl 0299.53028 · doi:10.14492/hokmj/1381758806
[383] Kazunari Yamauchi, ?On infinitesimal projective transformations satisfying certain conditions,?Hokkaido Math. J.,7, No. 1, 74?77 (1978). · Zbl 0383.53016 · doi:10.14492/hokmj/1381758492
[384] Kazunari Yamauchi, ?On infinitesimal projective transformations of a Riemannian manifold with constant scalar curvature,?Hokkaido Math. J.,8, No. 2, 167?175 (1979). · Zbl 0452.53024 · doi:10.14492/hokmj/1381758268
[385] Kazunari Yamauchi, ?Infinitesimal projective and conformai transformations in a tangent bundle,?Sci. Repts. Kagoshima Univ., No. 32, 47?58 (1983). · Zbl 0537.53014
[386] Kazunari Yamauchi, ?On infinitesimal projective transformations and infinitesimal conformai transformations in tangent bundles of Riemannian manifolds,?Sci. Repts. Kagoshima Univ., No. 36, 21?33 (1987). · Zbl 0633.53029
[387] Kentaro Yano, ?Concircular geometry, I?IV,?Proc. Acad. Japan,16, 195?200, 354?360, 442?448, 505?511 (1940). · Zbl 0024.08102 · doi:10.3792/pia/1195579139
[388] Kentaro Yano, ?Conformai transformations in Riemannian manifolds,?Ber. Math. Forschungsinst. Oberwohlfach, No. 4, 339?351 (1971). · Zbl 0221.53050
[389] Kentaro Yano, ?Notes on isometries,?Colloq. Math.,26, 1?7 (1972). · Zbl 0223.53018
[390] Kentaro Yano and Hitosi Hiramatu, ?Riemannian manifolds admitting an infinitesimal conformai transformation,?J. Diff. Geom.,10, No. 1, 23?38 (1975). · Zbl 0307.53024 · doi:10.4310/jdg/1214432673
[391] Kentaro Yano and Hitosi Hiramatu, ?On conformal changes of Riemannian metrics,?Kodai Math. Semin. Repts.,27, No. 1?2, 19?41 (1976). · Zbl 0328.53031 · doi:10.2996/kmj/1138847160
[392] Kentaro Yano and Hitosi Hiramatu, ?Isometry of Riemannian manifolds to spheres,?J. Diff. Geom.,12, No. 3, 443?460 (1977). · Zbl 0388.53011 · doi:10.4310/jdg/1214434095
[393] Makato Yawata, ?On the affine Killing vectors in the tangent bundles,?Rept. Chiba Inst. Technol., No. 29, 29?33 (1984).
[394] Ichiro Yokoto, ?Affine Killing vectors in the tangent bundles,?Kodai Math. J.,4, No. 3, 383?398 (1981). · Zbl 0494.53037 · doi:10.2996/kmj/1138036424
[395] Shinsuke Yorozu, ?Killing vector fields on noncompact Riemannian manifolds with boundary,?Kodai Math. J.,5, No. 3, 426?433 (1982). · Zbl 0504.53033 · doi:10.2996/kmj/1138036610
[396] Shinsuke Yorozu, ?Killing vector fields on complete Riemannian manifolds,?Proc. Amer. Math. Soc.,84, No. 1, 115?120 (1982). · Zbl 0477.53041 · doi:10.1090/S0002-9939-1982-0633291-1
[397] Shinsuke Yorozu, ?Affine and projective vector fields on complete non-compact Riemannian manifolds,?Yokohama Math. J.,31, No. 1?2, 41?46 (1983). · Zbl 0579.53035
[398] Shinsuke Yorozu, ?Conformai and Killing vector fields on complete noncompact Riemannian manifolds,? in:Geom., Geod. and Relat. Top. Proc. Symp., Tokyo, Nov. 29?Dec. 3, 1982, Amsterdam, Tokyo (1984), pp. 459?472. · Zbl 0477.53041
[399] Shinsuke Yorozu, ?The non-existence of Killing fields,?Tôhoku Math.,36, No. 1, 99?105 (1984). · Zbl 0536.53039 · doi:10.2748/tmj/1178228906
[400] Yashiro Yoshimatsu, ?On a theorem of Alekseevskii concerning conformai transformations,?J. Math. Soc. Jap.,28, No. 2, 278?289 (1976). · Zbl 0318.53043 · doi:10.2969/jmsj/02820278
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