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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold


Author: Bertram Kostant
Journal: Trans. Amer. Math. Soc. 80 (1955), 528-542
MSC: Primary 53.1X
DOI: https://doi.org/10.1090/S0002-9947-1955-0084825-8
MathSciNet review: 0084825
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  • W. Ambrose and I. M. Singer, A theorem on holonomy, Trans. Amer. Math. Soc. 75 (1953), 428–443. MR 63739, DOI https://doi.org/10.1090/S0002-9947-1953-0063739-1
  • Armand Borel and André Lichnerowicz, Espaces riemanniens et hermitiens symétriques, C. R. Acad. Sci. Paris 234 (1952), 2332–2334 (French). MR 48134
  • Armand Borel and André Lichnerowicz, Groupes d’holonomie des variétés riemanniennes, C. R. Acad. Sci. Paris 234 (1952), 1835–1837 (French). MR 48133
  • E. Cartan, Sur une classe remarquable d’espaces de Riemann, Bull. Soc. Math. France vol. 54 (1926) pp. 214-264; vol. 55 (1927) pp. 114-134. ---, La géométrie des groupes de transformations, J. Math. Pures Appl. vol. 6 (1927) pp. 1-119.
  • Robert Hermann, Sur les isométries infinitésimales et le groupe d’holonomie d’un espace de Riemann, C. R. Acad. Sci. Paris 239 (1954), 1178–1180 (French). MR 66737
  • Robert Hermann, Sur les automorphismes infinitésimaux d’une $G$-structure, C. R. Acad. Sci. Paris 239 (1954), 1760–1761 (French). MR 66738
  • Albert Nijenhuis, On the holonomy groups of linear connections. II. Properties of general linear connections, Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indagationes Math. 16 (1954), 17–25. MR 0063738
  • Katsumi Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33–65. MR 59050, DOI https://doi.org/10.2307/2372398
  • Katsumi Nomizu, Sur les transformations affines d’une variété riemannienne, C. R. Acad. Sci. Paris 237 (1953), 1308–1310 (French). MR 59047
  • ---, Applications de l’étude de transformation affine aux espaces homogeneous reimanniens, C. R. Acad. Sci. Paris vol. 237 (1953) pp. 1386-1387.
  • André Lichnerowicz, Espaces homogènes kählériens, Géométrie différentielle. Colloque Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1953, Centre National de la Recherche Scientifique, Paris, 1953, pp. 171–184 (French). MR 0066017
  • K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. MR 0062505

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Article copyright: © Copyright 1955 American Mathematical Society