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 $\Omega (M^n)$ with the $L^2$ (weak) Riemannian structure.
Citation
Leonardo Biliotti. "The exponential map of a weak Riemannian Hilbert manifold." Illinois J. Math. 48 (4) 1191 - 1206, Winter 2004. https://doi.org/10.1215/ijm/1258138506
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