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Geometry II pp 139-248 | Cite as

Discrete Groups of Motions of Spaces of Constant Curvature

  • E. B. Vinberg
  • O. V. Shvartsman
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 29)

Abstract

Discrete groups of motions of spaces of constant curvature, as well as other groups that can be regarded as such (although they may be defined differently), arise naturally in different areas of mathematics and its applications. Examples are the symmetry groups of regular polyhedra, symmetry groups of ornaments and crystallographic structures, discrete groups of holomorphic transformations arising in the uniformization theory of Riemannian surfaces, fundamental groups of space forms, groups of integer Lorentz transformations etc. (see Chapter 1). Their study fills a brilliant page in the development of geometry.

Keywords

Constant Curvature Discrete Group Fundamental Domain Finite Index Fuchsian Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1993

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  • E. B. Vinberg
  • O. V. Shvartsman

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