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Kostant, Bertram

Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold. (English) Zbl 0066.16001

Trans. Am. Math. Soc. 80, 528-542 (1955).
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Keywords:

Riemannian manifolds
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\textit{B. Kostant}, Trans. Am. Math. Soc. 80, 528--542 (1955; Zbl 0066.16001)
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References:

[1] W. Ambrose and I. M. Singer, A theorem on holonomy, Trans. Amer. Math. Soc. 75 (1953), 428 – 443. · Zbl 0052.18002
[2] Armand Borel and André Lichnerowicz, Espaces riemanniens et hermitiens symétriques, C. R. Acad. Sci. Paris 234 (1952), 2332 – 2334 (French). · Zbl 0046.39803
[3] Armand Borel and André Lichnerowicz, Groupes d’holonomie des variétés riemanniennes, C. R. Acad. Sci. Paris 234 (1952), 1835 – 1837 (French). · Zbl 0046.39801
[4] 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. · JFM 53.0390.01
[5] -, La géométrie des groupes de transformations, J. Math. Pures Appl. vol. 6 (1927) pp. 1-119.
[6] 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). · Zbl 0056.41103
[7] Robert Hermann, Sur les automorphismes infinitésimaux d’une \?-structure, C. R. Acad. Sci. Paris 239 (1954), 1760 – 1761 (French). · Zbl 0058.16003
[8] 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. · Zbl 0055.40703
[9] Katsumi Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33 – 65. · Zbl 0059.15805
[10] Katsumi Nomizu, Sur les transformations affines d’une variété riemannienne, C. R. Acad. Sci. Paris 237 (1953), 1308 – 1310 (French). · Zbl 0051.12902
[11] -, Applications de l’étude de transformation affine aux espaces homogeneous reimanniens, C. R. Acad. Sci. Paris vol. 237 (1953) pp. 1386-1387. · Zbl 0052.17505
[12] 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). · Zbl 0053.11603
[13] K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. · Zbl 0051.39402
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