Skip to main content
SpringerLink
Log in

Geometry II

Spaces of Constant Curvature

  • Book
  • © 1993

Overview

Editors:
  1. E. B. Vinberg

    1. Department of Mathematics, Moscow University, Moscow, Russia

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 29)

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 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 159.99
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 (2 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Geometry of Spaces of Constant Curvature

    • D. V. Alekseevskij, E. B. Vinberg, A. S. Solodovnikov
    Pages 1-138

  3. Discrete Groups of Motions of Spaces of Constant Curvature

    • E. B. Vinberg, O. V. Shvartsman
    Pages 139-248

  4. Back Matter

    Pages 249-256
    Download chapter PDF
Back to top

Keywords

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.

Editors and Affiliations

  • Department of Mathematics, Moscow University, Moscow, Russia

    E. B. Vinberg

Bibliographic Information

  • Book Title: Geometry II

  • Book Subtitle: Spaces of Constant Curvature

  • Editors: E. B. Vinberg

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-662-02901-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-52000-9Published: 25 June 1993

  • Softcover ISBN: 978-3-642-08086-9Published: 22 September 2011

  • eBook ISBN: 978-3-662-02901-5Published: 17 April 2013

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: IX, 256

  • Number of Illustrations: 10 b/w illustrations

  • Additional Information: Original Russian edition published by Publisher VINITI, Moscow, 1988

  • Topics: Geometry, Topology, Group Theory and Generalizations, Analysis, Topological Groups, Lie Groups

Publish with us

Policies and ethics

Back to top

Search

Navigation