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Part of the book series: Springer Monographs in Mathematics (SMM)
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About this book
This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n :::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gauß had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries withwell-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten sion of index 2 of the group PSL(2,
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Groups Acting on Hyperbolic Space
Book Subtitle: Harmonic Analysis and Number Theory
Authors: Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-662-03626-6
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1998
Hardcover ISBN: 978-3-540-62745-6Published: 12 November 1997
Softcover ISBN: 978-3-642-08302-0Published: 15 December 2010
eBook ISBN: 978-3-662-03626-6Published: 09 March 2013
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XV, 524
Topics: Group Theory and Generalizations, Special Functions, Number Theory, Global Analysis and Analysis on Manifolds