Projective and Cayley-Klein Geometries

  • Arkady L. Onishchik
  • Rolf Sulanke

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

Table of contents

  1. Front Matter
    Pages I-XV
  2. Pages 1-131
  3. Pages 133-402
  4. Back Matter
    Pages 403-432

About this book


Projective geometry, and the Cayley-Klein geometries embedded into it, were originated in the 19th century. It is one of the foundations of algebraic geometry and has many applications to differential geometry.

The book presents a systematic introduction to projective geometry as based on the notion of vector space, which is the central topic of the first chapter. The second chapter covers the most important classical geometries which are systematically developed following the principle founded by Cayley and Klein, which rely on distinguishing an absolute and then studying the resulting invariants of geometric objects.

An appendix collects brief accounts of some fundamental notions from algebra and topology with corresponding references to the literature.

This self-contained introduction is a must for students, lecturers and researchers interested in projective geometry.



Cayley-Klein Geometry Classical Groups Elliptic Geometry Finite Homogenous Spaces Hyperbolic Geometry Invariant Möbius Geometry Projective Geometry Symplectic Geometry Topology Transformation Groups algebra geometry

Authors and affiliations

  • Arkady L. Onishchik
    • 1
  • Rolf Sulanke
    • 2
  1. 1.Faculty of MathematicsYaroslavl State UniversityYaroslavlRussia
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-35644-8
  • Online ISBN 978-3-540-35645-5
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site