© 2006

Projective and Cayley-Klein Geometries

  • Systematic development of the subject from the current point of view


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

  1. 1.Faculty of MathematicsYaroslavl State UniversityYaroslavlRussia
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

Bibliographic information

  • Book Title Projective and Cayley-Klein Geometries
  • Authors Arkadij L. Onishchik
    Rolf Sulanke
  • Series Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-540-35644-8
  • Softcover ISBN 978-3-642-07134-8
  • eBook ISBN 978-3-540-35645-5
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages XVI, 434
  • Number of Illustrations 69 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site


From the reviews:

"This book is a comprehensive account of projective geometry and other classical geometries … exhaustively covering all the details that anyone could ever ask for. It is well-written and the many exercises and many figures … make it a very usable text. … My proposed audience for this book coincides with the publisher’s advice: graduate students and researchers in mathematics will find this book most useful … . For these readers, the book is a jewel long yearned for, and finally found." (Gizem Karaali, MathDL, November, 2007)