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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The normal holonomy group

Author: Carlos Olmos
Journal: Proc. Amer. Math. Soc. 110 (1990), 813-818
MSC: Primary 53C40; Secondary 53C35
MathSciNet review: 1023346
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Abstract: We prove that the restricted normal holonomy group of a submanifold of a space of constant curvature is compact and that the nontrivial part of its representation on the normal space is the isotropy representation of a semisimple Riemannian symmetric space.

References [Enhancements On Off] (What's this?)

  • [B] Marcel Berger, Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France 83 (1955), 279–330 (French). MR 0079806
  • [K-N] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. MR 0152974
  • [S] James Simons, On the transitivity of holonomy systems, Ann. of Math. (2) 76 (1962), 213–234. MR 0148010
  • [S-O] C. Olmos and C. Sanchez, A geometric characterization of $ R$-spaces, preprint.

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Keywords: Normal connection, holonomy group, normal curvature tensor
Article copyright: © Copyright 1990 American Mathematical Society