Groups Acting on Hyperbolic Space
Harmonic Analysis and Number Theory
Authors: Elstrodt, Juergen, Grunewald, Fritz, Mennicke, Jens
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- About this book
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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,
- Table of contents (10 chapters)
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Three-Dimensional Hyperbolic Space
Pages 1-32
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Groups Acting Discontinuously on Three-Dimensional Hyperbolic Space
Pages 33-81
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Automorphic Functions
Pages 83-129
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Spectral Theory of the Laplace Operator
Pages 131-183
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Spectral Theory of the Laplace Operator for Cocompact Groups
Pages 185-229
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Groups Acting on Hyperbolic Space
- Book Subtitle
- Harmonic Analysis and Number Theory
- Authors
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- Juergen Elstrodt
- Fritz Grunewald
- Jens Mennicke
- Series Title
- Springer Monographs in Mathematics
- Copyright
- 1998
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-662-03626-6
- DOI
- 10.1007/978-3-662-03626-6
- Hardcover ISBN
- 978-3-540-62745-6
- Softcover ISBN
- 978-3-642-08302-0
- Series ISSN
- 1439-7382
- Edition Number
- 1
- Number of Pages
- XV, 524
- Topics
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