Properly discontinuous actions on Hilbert manifolds

2013/09/16 by Biliotti, Leonardo, Francesco, Mercuri
#57S25 #58B99 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.4006

Abstract

In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get examples of complete infinite dimensional Kähler manifolds with positive holomorphic sectional curvature and infinite fundamental group in contrast with the finite dimensional case and we classify abelian groups acting linearly, isometrically and properly discontinuously on Stiefel manifolds. Finally, we classify homogeneous Hilbert manifolds with constant sectional curvature.

Related

• Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces
• Properly discontinuous isometric group actions on inhomogeneous\n Lorentzian manifolds
• Nonnegative curvature, symmetry and fundamental group
• Riemannian Hilbert manifolds
• Around groups in Hilbert Geometry