IJPAM: Volume 25, No. 1 (2005)
Department of Mathematics
No. 181, Section 3, Taichung-Kam Road
Taichung, 407-04, TAIWAN, R.O.C.
Abstract.In this short note we develop the notion of Hausdorff distance between the discrete subgroups of the isometry group on a simply connected Riemannian manifold with lower curvature bounds. We prove a rigidity theorem to show that close geometric structures will imply close group structures.
Received: August 3, 2005
AMS Subject Classification: 53C20, 57S25
Key Words and Phrases: curvature, discrete groups, Hausdorff distance
Source: International Journal of Pure and Applied Mathematics