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Geometry II pp 1-138 | Cite as

Geometry of Spaces of Constant Curvature

  • D. V. Alekseevskij
  • E. B. Vinberg
  • A. S. Solodovnikov
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 29)

Abstract

Spaces of constant curvature, i.e. Euclidean space, the sphere, and Lobachevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition.

Keywords

Riemannian Manifold Dihedral Angle Homogeneous Space Constant Curvature Vector Model 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • D. V. Alekseevskij
  • E. B. Vinberg
  • A. S. Solodovnikov

There are no affiliations available

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