Geodesic
ISOMETRIES AND DISCRETE ISOMETRY SUBGROUPS OF HYPERBOLIC SPACES
Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 31-38

Voir la notice de l'article provenant de la source Cambridge University Press

Let n be the n-dimensional hyperbolic space with n ≥ 2. Suppose that G is a discrete, sense-preserving subgroup of Isomn, the isometry group of n. Let p be the projection map from n to the quotient space M = n/G. The first goal of this paper is to prove that for any a ∈ ∂n (the sphere at infinity of n), there exists an open neighbourhood U of a in n ∪ ∂ n such that p is an isometry on U ∩ n if and only if a ∈ oΩ(G) (the domain of proper discontinuity of G). This is a generalization of the main result discussed in the work by Y. D. Kim (A theorem on discrete, torsion free subgroups of Isomn, Geometriae Dedicata109 (2004), 51–57). The second goal is to obtain a new characterization for the elements of Isomn by using a class of hyperbolic geometric objects: hyperbolic isosceles right triangles. The proof is based on a geometric approach.
DOI : 10.1017/S0017089508004503
Mots-clés : Primary: 30F35, 51M10, Secondary: 20H10, 22E40 
FU, XI; WANG, XIANTAO. ISOMETRIES AND DISCRETE ISOMETRY SUBGROUPS OF HYPERBOLIC SPACES. Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 31-38. doi: 10.1017/S0017089508004503
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