Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the construction of a certain class of Kleinian groups


Author: Ricardo Bianconi
Journal: Proc. Amer. Math. Soc. 123 (1995), 3119-3124
MSC: Primary 30F40; Secondary 20H10
DOI: https://doi.org/10.1090/S0002-9939-1995-1277097-0
MathSciNet review: 1277097
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if $\{ {S_1},{S_1}’, \ldots ,{S_n},S_n’\}$ is a collection of distinct spheres in ${\mathbb {R}^m}$ with common exterior, and ${g_1}, \ldots ,{g_n}$ are Möbius transformations such that for each i, ${S_i}$ is the isometric sphere of ${g_i}$ and $S_i’$ is the isometric sphere of $g_i^{ - 1}$ and such that ${g_i}$ maps points of contact of ${S_i}$, to points of contact of $S_i’$, then the group G generated by the ${g_i}$’s is Kleinian.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30F40, 20H10

Retrieve articles in all journals with MSC: 30F40, 20H10


Additional Information

Keywords: Kleinian groups, parabolic, infinite cycle transformations, isometric spheres, Poincaré’s Polyhedron Theorem
Article copyright: © Copyright 1995 American Mathematical Society