Some Results on Infinite Dimensional Riemannian Geometry

Details Some Results on Infinite Dimensional Riemannian Geometry Some Results on Infinite Dimensional Riemannian Geometry

2003-04-18

arxiv.org/abs/math/0304256v2

Mathematics

Differential Geometry

27 pages, no figures

Scientific paper

In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index Lemma that we will allow us to extend some classical results of finite dimensional Riemannian geometry such as Rauch and Berger Theorems and the Topogonov Theorem in the class of manifolds on which the Hopf-Rinow Theorem holds.

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