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 constant 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.
Properly discontinuous isometric actions on the unit sphere of infinite dimensional Hilbert spaces / BILIOTTI L.. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 26(2004), pp. 385-395.