The exponential map of a weak Riemannian Hilbert manifold

Abstract

We prove the Focal Index Lemma and the Rauch-Berger Comparison Theorems on a weak Riemannian Hilbert manifold with a smooth Levi-Civita connection and we apply these results to the free loop space Ω(Mn) with the L2 (weak) Riemannian structure. ©2004 University of Illinois.