Groups Acting on Hyperbolic Space - Harmonic Analysis and Number Theory (Hardcover, 1998 ed.)

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 with well-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,"

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Springer Monographs in Mathematics
Release date:	November 1997
First published:	1998
Authors:	Juergen Elstrodt • Fritz Grunewald • Jens Mennicke
Dimensions:	235 x 155 x 35mm (L x W x T)
Format:	Hardcover
Pages:	524
Edition:	1998 ed.
ISBN-13:	978-3-540-62745-6
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-540-62745-6
Barcode:	9783540627456

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