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

摘要

We study the properly discontinuous and isometric actions on the unit sphereof infinite dimensional Hilbert spaces and we get some new examples of Hilbertmanifold with costant positive sectional curvature. We prove some necessaryconditions for a group to act isometrically and properly discontinuously and inthe case of finitely generated Abelian groups, the necessary and sufficientconditions are given.