Guillemin, Victor W.; Sternberg, Shlomo An algebraic model of transitive differential geometry. (English) Zbl 0121.38801 Bull. Am. Math. Soc. 70, 16-47 (1964). Reviewer: Robert Hermann Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 123 Documents MSC: 53Cxx Global differential geometry Keywords:Riemannian manifolds × Cite Format Result Cite Review PDF Full Text: DOI References: [1] U. Amaldi, Introducione alla teoria dei gruppi continui infiniti di transformazioni. I, II, Librería del Univ. de Roma, Rome, 1942, 1944. [2] Daniel Bernard, Sur la géométrie différentielle des \?-structures, Ann. Inst. Fourier Grenoble 10 (1960), 151 – 270 (French). · Zbl 0095.36406 [3] Élie Cartan, Sur la structure des groupes infinis de transformation, Ann. Sci. École Norm. Sup. (3) 21 (1904), 153 – 206 (French). · JFM 35.0176.04 [4] Elie Cartan, Les sous-groupes des groupes continus de transformations, Ann. Sci. École Norm. Sup. (3) 25 (1908), 57 – 194 (French). · JFM 39.0206.04 [5] Elie Cartan, Les groupes de transformations continus, infinis, simples, Ann. Sci. École Norm. Sup. (3) 26 (1909), 93 – 161 (French). · JFM 40.0193.02 [6] Elie Cartan, Œuvres complètes. Partie II. Vol. 1. Algèbre, formes différentielles, systèmes différentiels. Vol. 2. Groupes infinis, systèmes différentiels, théories d’équivalence, Gauthier-Villars, Paris, 1953 (French). · Zbl 0058.08302 [7] Elie Cartan, Œuvres complètes. Partie II. Vol. 1. Algèbre, formes différentielles, systèmes différentiels. Vol. 2. Groupes infinis, systèmes différentiels, théories d’équivalence, Gauthier-Villars, Paris, 1953 (French). · Zbl 0058.08302 [8] Élie Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Actualités Sci. Ind., no. 994, Hermann et Cie., Paris, 1945 (French). · Zbl 0211.12701 [9] Shiing-Shen Chern, Pseudo-groupes continus infinis, Géométrie différentielle., Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, vol. 1953, Centre National de la Recherche Scientifique, Paris, 1953, pp. 119 – 136 (French). · Zbl 0053.01604 [10] Shiing-shen Chern, An elementary proof of the existence of isothermal parameters on a surface, Proc. Amer. Math. Soc. 6 (1955), 771 – 782. · Zbl 0066.15402 [11] Shiing-shen Chern, On a generalization of Kähler geometry, Algebraic geometry and topology. A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N. J., 1957, pp. 103 – 121. · Zbl 0078.14103 [12] Charles Ehresmann, Structures locales et structures infinitésimales, C. R. Acad. Sci. Paris 234 (1952), 587 – 589 (French). · Zbl 0046.40703 [13] Charles Ehresmann, Introduction à la théorie des structures infinitésimales et des pseudo-groupes de Lie, Géométrie différentielle. Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1953, Centre National de la Recherche Scientifique, Paris, 1953, pp. 97 – 110 (French). · Zbl 0052.39803 [14] Charles Ehresmann, Structures locales, Ann. Mat. Pura Appl. (4) 36 (1954), 133 – 142 (French). · Zbl 0055.42002 · doi:10.1007/BF02412835 [15] V. W. Guillemin, The geometry of G-structures of finite type, thesis, Harvard Univ., Cambridge, Mass., 1962. [16] Victor W. Guillemin and Shlomo Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc. 70 (1964), 16 – 47. · Zbl 0121.38801 [17] E. Kähler, Einfuhrung in die Theorie der Systeme von Differentialgleichungen, Chelsea, New York, 1949. [18] Masatake Kuranishi, On E. Cartan’s prolongation theorem of exterior differential systems, Amer. J. Math. 79 (1957), 1 – 47. · Zbl 0077.29701 · doi:10.2307/2372381 [19] Masatake Kuranishi, On the local theory of continuous infinite pseudo groups. I, Nagoya Math. J 15 (1959), 225 – 260. · Zbl 0212.56501 [20] Paulette Libermann, Sur le problème d’équivalence de certaines structures infinitésimales, Ann. Mat. Pura Appl. (4) 36 (1954), 27 – 120 (French). · Zbl 0056.15401 · doi:10.1007/BF02412833 [21] Paulette Libermann, Pseudo groupes infinitésimaux. Applications aux \?-structures, C. R. Acad. Sci. Paris 246 (1958), 1365 – 1368 (French). · Zbl 0095.16201 [22] S. Lie, Gesammelte Abhandlungen, Band VI, pp. 300-365, Orlo, Leipzig, 1927. [23] Y. Matsushima, Pseudogroupes de Lie transitifs, Séminaire Bourbaki, no. 118, Hermann, Paris, 1955. [24] Y. Matsushima, Sur les algèbres de Lie linéaires semi-involutives, Colloque de topologie de Strasbourg, 1954. · Zbl 0068.02801 [25] A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math. (2) 65 (1957), 391 – 404. · Zbl 0079.16102 · doi:10.2307/1970051 [26] J.-P. Serre, Algèbre locale, mimeographed notes, Paris. · Zbl 0091.03701 [27] I. M. Singer and S. Sternberg, On the infinite groups of Lie and Cartan. I (to appear). · Zbl 0277.58008 [28] D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I. Infinitesimal deformations of structure, Ann. of Math. (2) 76 (1962), 306 – 398. , https://doi.org/10.2307/1970277 D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. II. Deformations of structure, Ann. of Math. (2) 76 (1962), 399 – 445. · Zbl 0124.38601 · doi:10.2307/1970367 [29] Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. · Zbl 0129.13102 [30] Ryoyu Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev. (2) 101 (1956), 1597 – 1607. · Zbl 0070.22102 [31] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. · Zbl 0322.13001 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.