(1) Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY, 11794-3651, U.S.A.
Abstract:
Let Hn be the hyperbolic n-space with n⩾ 2. Suppose that Γ H n is a discrete, torsion free subgroup and a is a point in the domain of discontinuity Ω (Γ). Let p be the projection map from Hn to the quotient manifold M=Hn/Γ. In this paper we prove that there exists an open neighborhood U of a in Hn∪ Ω (Γ) such that p is an isometry on U∩ Hn.Mathematics Subject Classification (2000). primary: 51M10; secondary: 22E40, 57M50.