Encyclopaedia of Mathematical Sciences

Geometry II

Spaces of Constant Curvature

Editors: Vinberg, E.B. (Ed.)

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About this book

Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba­ chevskij 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. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space. Lobachevskij geometry, which in the first fifty years after its discovery had been regarded only as a logically feasible by-product appearing in the investigation of the foundations of geometry, has even now, despite the fact that it has found its use in numerous applications, preserved a kind of exotic and even romantic element. This may probably be explained by the permanent cultural and historical impact which the proof of the independence of the Fifth Postulate had on human thought.

Table of contents (2 chapters)

  • Geometry of Spaces of Constant Curvature

    Alekseevskij, D. V. (et al.)

    Pages 1-138

  • Discrete Groups of Motions of Spaces of Constant Curvature

    Vinberg, E. B. (et al.)

    Pages 139-248

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-662-02901-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-540-52000-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-08086-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry II
Book Subtitle
Spaces of Constant Curvature
Editors
  • E.B. Vinberg
Translated by
Minachin, V.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
29
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-02901-5
DOI
10.1007/978-3-662-02901-5
Hardcover ISBN
978-3-540-52000-9
Softcover ISBN
978-3-642-08086-9
Series ISSN
0938-0396
Edition Number
1
Number of Pages
IX, 256
Number of Illustrations and Tables
10 b/w illustrations
Additional Information
Original Russian edition published by Publisher VINITI, Moscow, 1988
Topics