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Springer Monographs in Mathematics

Groups Acting on Hyperbolic Space

Harmonic Analysis and Number Theory

Authors: Elstrodt, Juergen, Grunewald, Fritz, Mennicke, Jens

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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 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)

Table of contents (10 chapters)

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-3-662-03626-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
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Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-540-62745-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-642-08302-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Groups Acting on Hyperbolic Space
Book Subtitle
Harmonic Analysis and Number Theory
Authors
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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