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Proceedings of the American Mathematical Society
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1023346-9
PII: S 0002-9939(1990)1023346-9
Keywords: Normal connection, holonomy group, normal curvature tensor
Article copyright: © Copyright 1990 American Mathematical Society