Illinois Journal of Mathematics

The exponential map of a weak Riemannian Hilbert manifold

Leonardo Biliotti

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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.

Article information

Source
Illinois J. Math., Volume 48, Number 4 (2004), 1191-1206.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138506

Digital Object Identifier
doi:10.1215/ijm/1258138506

Mathematical Reviews number (MathSciNet)
MR2113672

Zentralblatt MATH identifier
1083.58009

Subjects
Primary: 58B20: Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]
Secondary: 58D15: Manifolds of mappings [See also 46T10, 54C35]

Citation

Biliotti, Leonardo. The exponential map of a weak Riemannian Hilbert manifold. Illinois J. Math. 48 (2004), no. 4, 1191--1206. doi:10.1215/ijm/1258138506. https://projecteuclid.org/euclid.ijm/1258138506


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