Groups Acting on Hyperbolic Space Harmonic Analysis and Number Theor
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 ana
- PDF / 41,218,015 Bytes
- 530 Pages / 439 x 666 pts Page_size
- 100 Downloads / 272 Views
Springer-Verlag Berlin Heidelberg GmbH
J. Elstrodt
F. Grunewald
J. Mennicke
Groups Acting on Hyperbolic Space Harmonie Analysis and Number Theory
,
Springer
Jürgen Elstrodt Universität Münster Mathematisches Institut Einsteinstraße 62 D-48149 Münster Fritz Grunewald Universität Düsseldorf Mathematisches Institut Universitätsstraße 1 D-40225 Düsseldorf Jens Mennicke Universität Bielefeld Fakultät für Mathematik Universitätsstraße 25 D-33615 Bielefeld
CIP data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Elstrodt,Jürgen: Groups acting on hyperbolic space: harmonic analysis and number theory I /. Elstrodt; F. Grunewald; /. Mennicke. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1997 (Springer monographs in mathematics)
Mathematics Subject Classification (1991): llF72, llF55, l1E39, llE45, llE45, llM26, 20F55, 20F55, 20H05, 58C40
ISBN 978-3-642-08302-0
ISBN 978-3-662-03626-6 (eBook)
DOI 10.1007/978-3-662-03626-6 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its CUTTent version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998
Originally published by Springer-Verlag Berlin Heidelberg New York in 1998. Softcover reprint of the hardcover 1 st edition 1998 The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the authors using a Springer TEX macro package 41/3143-543210 - Printed on acid-free paper SPIN 10467814
Dedicated to the Memory of Hans Maaß 1911-1992
Preface
This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curvature -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 geometries 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 coordin
