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Geometriae Dedicata

, Volume 109, Issue 1, pp 51–57 | Cite as

A Theorem on Discrete, Torsion Free Subgroups of Isom H n

To my wife, Inae Park and my daughter, Yoonsuh Kim
  • Young Deuk Kim
Article

Abstract

Let H n be the hyperbolic n-space with n⩾ 2. Suppose that Γ <Isom 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 H n to the quotient manifold M=H n /Γ. In this paper we prove that there exists an open neighborhood U of a in H n ∪ Ω (Γ) such that p is an isometry on UH n .

Keywords

torsion free subgroup domain of discontinuity 

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References

  1. 1.
    Beardon, A.F. 1983The Geometry of Discrete GroupsSpringer-VerlagNew YorkGoogle Scholar
  2. 2.
    Maskit, B. 1988Kleinian GroupsSpringer-VerlagBerlin HeidelbergGoogle Scholar
  3. 3.
    Ratcli.e, J.G. 1994Foundations of Hyperbolic ManifoldsSpringer-VerlagNew YorkGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of MathematicsState University of New York at Stony BrookStony BrookU.S.A.

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