Riemannian Hilbert manifolds

TL;DR

This paper discusses advanced geometric properties of Riemannian Hilbert manifolds, including singularities, completeness, homogeneity, and extends classical theorems to infinite dimensions.

Contribution

It extends a classical theorem by Nomizu and Ozeki to the setting of infinite-dimensional Riemannian Hilbert manifolds and discusses various geometric properties.

Findings

Analysis of exponential map singularities

Results on completeness and homogeneity

Extension of Nomizu and Ozeki's theorem

Abstract

In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert quotient manifolds. We also extend a Theorem due to Nomizu and Ozeki to infinite dimensional Riemannian Hilbert manifolds.