Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces

Details Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces

2003-04-14

arxiv.org/abs/math/0304177v1

Mathematics

Differential Geometry

11 pages, no figueres

Scientific paper

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.

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