Skip to main content
SpringerLink
Log in

Groups Acting on Hyperbolic Space

Harmonic Analysis and Number Theory

  • Book
  • © 1998

Overview

Authors:
  1. Jürgen Elstrodt

    1. Mathematisches Institut, Universität Münster, Münster, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Fritz Grunewald

    1. Mathematisches Institut, Universität Düsseldorf, Düsseldorf, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Jens Mennicke

    1. Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • The book covers a lot of ground: The authors have worked on it for over 10 years
  • It has no competitor
  • The subject is a very lively and productive area of research that has a high degree of maturity nevertheless

Part of the book series: Springer Monographs in Mathematics (SMM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Three-Dimensional Hyperbolic Space

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 1-32

  3. Groups Acting Discontinuously on Three-Dimensional Hyperbolic Space

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 33-81

  4. Automorphic Functions

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 83-129

  5. Spectral Theory of the Laplace Operator

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 131-183

  6. Spectral Theory of the Laplace Operator for Cocompact Groups

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 185-229

  7. Spectral Theory of the Laplace Operator for Cofinite Groups

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 231-310

  8. PSL(2) over Rings of Imaginary Quadratic Integers

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 311-357

  9. Eisenstein Series for PSL(2) over Imaginary Quadratic Integers

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 359-405

  10. Integral Binary Hermitian Forms

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 407-441

  11. Examples of Discontinuous Groups

    • Jürgen Elstrodt, Fritz Grunewald, Jens Mennicke
    Pages 443-495

  12. Back Matter

    Pages 497-524
    Download chapter PDF
Back to top

Keywords

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,

Authors and Affiliations

  • Mathematisches Institut, Universität Münster, Münster, Germany

    Jürgen Elstrodt

  • Mathematisches Institut, Universität Düsseldorf, Düsseldorf, Germany

    Fritz Grunewald

  • Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany

    Jens Mennicke

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation