The normal holonomy group
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- by Carlos Olmos PDF
- Proc. Amer. Math. Soc. 110 (1990), 813-818 Request permission
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
- 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 79806
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
- James Simons, On the transitivity of holonomy systems, Ann. of Math. (2) 76 (1962), 213–234. MR 148010, DOI 10.2307/1970273 C. Olmos and C. Sanchez, A geometric characterization of $R$-spaces, preprint.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 813-818
- MSC: Primary 53C40; Secondary 53C35
- DOI: https://doi.org/10.1090/S0002-9939-1990-1023346-9
- MathSciNet review: 1023346