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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] M. Berger, Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés Riemannienes, Bull. Soc. Math. France 83 (1955), 279, 230. MR 0079806 (18:149a)
  • [K-N] S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. I, Interscience Publishers, 1963. MR 0152974 (27:2945)
  • [S] J. Simons, On the transitivity of holonomy systems, Ann. of Math. (2) 76 (1962). MR 0148010 (26:5520)
  • [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

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