Riemannian metrics on an infinite dimensional symplectic group
Differential Geometry
2015-03-30 v1 Operator Algebras
Abstract
The aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe's classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.
Keywords
Cite
@article{arxiv.1503.08186,
title = {Riemannian metrics on an infinite dimensional symplectic group},
author = {Manuel López Galván},
journal= {arXiv preprint arXiv:1503.08186},
year = {2015}
}
Comments
18 pages. The final version of this preprint will appear in Journal of Mathematical Analysis and Applications