Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces
Differential Geometry
2007-05-23 v1
Abstract
We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case of finitely generated Abelian groups, the necessary and sufficient conditions are given.
Keywords
Cite
@article{arxiv.math/0304177,
title = {Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces},
author = {Leonardo Biliotti},
journal= {arXiv preprint arXiv:math/0304177},
year = {2007}
}
Comments
11 pages, no figueres