Exponential map of a weak Riemannian Hilbert manifold

2004/02/12 by Leonardo Biliotti, Biliotti, Leonardo
Mathematics · Physics and Astronomy · #22E65 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 58B20 secondary 58D15 #math.DG #msc:22E65 #msc:58B20 #msc:58D15

paper · pdf · doi:10.48550/arxiv.math/0402207

12 pages

openalex publication_date 2004/02/12 · arxiv created 2006/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Focal Index Lemma and the Rauch and Berger comparison theorems on a weak Riemannian Hilbert manifold with a smooth Levi-Civita connection and we apply these results to the free loop spaces of a compact manifold with the L² metrics

Citations

• Curvatures of left invariant metrics on lie groups

Related

• Some Results on Infinite Dimensional Riemannian Geometry
• Riemannian Hilbert manifolds
• The Completion of the Manifold of Riemannian Metrics with Respect to its L² Metric
• Weak Riemannian manifolds from finite index subfactors
• Levi-Civita connections of flag manifolds