zbMATH — the first resource for mathematics

Pseudoconformally-flat and pseudo-flat quasi-Sasakian manifolds. (English. Russian original) Zbl 1180.53029
Russ. Math. 53, No. 12, 59-62 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 12, 69-73 (2009).
Summary: We consider the theory of pseudoconformally-flat (i.e., simultaneously contactly selfdual and contactly anti-selfdual) and pseudo-flat (i.e., simultaneously contactly $$R$$-selfdual and contactly $$R$$-anti-selfdual) 5-dimensional quasi-Sasakian manifolds.
MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
Full Text:
References:
 [1] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, ”Self-Duality in Four-Dimensional Riemannian Geometry,” Proc. Roy. Soc. London. Ser. A. 362, 425–461 (1978). · Zbl 0389.53011 · doi:10.1098/rspa.1978.0143 [2] B. Y. Chen, ”Some Topological Obstructions to Bochner-Kähler Metrics and Their Applications,” J. Diff. Geom. 13, 547–558 (1978). · Zbl 0354.53049 · doi:10.4310/jdg/1214434707 [3] J.-P. Bourguignon, ”Les Variétés de Dimension 4 à Signature non Nulle Dont la Courbure est Harmonique sont d’Einstein,” Invent. Math. 63, 263–286 (1981). · Zbl 0456.53033 · doi:10.1007/BF01393878 [4] A. Derdzinski, ”Self-Duality of Kähler Manifolds and Einstein Manifolds of Dimensional Four,” Compos. Math. 49, 405–433 (1983). · Zbl 0527.53030 [5] M. Itoh, ”Self-Duality of Kähler Surfaces,” Compos. Math. 51, 265–273 (1984). · Zbl 0546.53044 [6] O. E. Arsen’eva, ”Selfdual Geometry of Generalized Kählerian Manifolds,” Matem. Sborn. 184(8), 137–148 (1993). [7] O. E. Arsen’eva and V. F. Kirichenko, ”Self-Dual Geometry of Generalized Hermitian Surfaces,” Matem. Sborn. 189(1), 21–44 (1998). · Zbl 0907.53023 [8] A. Besse, Einstein Manifolds (Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987; Mir, Moscow, 1990), Vols. 1–2. [9] R. Penrose, ”The Twistor Programme,” Math. Phys. Repts. 12, 65–76 (1977). · doi:10.1016/0034-4877(77)90047-7 [10] A. V. Aristarkhova and V. F. Kirichenko, ”Contact Selfdual Geometry of 5-Dimensional Quasi-Sasakian Manifolds,” Izv. Ross. Akad. Nauk. Ser. Matem. (in press). · Zbl 1282.53022 [11] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds (Progr. in Math., Berlin: Birkhauser-Boston-Basel, 2003). [12] V. F. Kirichenko, Differential-Geometric Structures on Manifolds (Mosk. Ped. Gos. Univ., Moscow, 2003) [in Russian]. [13] P. K. Rashevskii, Riemannian Geometry and Tensor Analysis (Nauka, Moscow, 1967) [in Russian]. [14] D. E. Blair, ”The Theory of Quasi-Sasakian Structures,” J. Diff. Geom. 1, 331–345 (1967). · Zbl 0163.43903 · doi:10.4310/jdg/1214428097 [15] V. F. Kirichenko and A. R. Rustanov, ”Differential Geometry of Quasi-Sasakian Manifolds,” Matem. Sborn. 193(8), 71–100 (2002). · Zbl 1066.53130
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.