Some Results on Infinite Dimensional Riemannian Geometry
Differential Geometry
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/0304256,
title = {Some Results on Infinite Dimensional Riemannian Geometry},
author = {Leonardo Biliotti},
journal= {arXiv preprint arXiv:math/0304256},
year = {2007}
}
Comments
27 pages, no figures