Projective differential geometry old and new : from the Schwarzian derivative to the cohomology of diffeomorphism groups /

Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and p...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Ovsienko, Valentin
Other Authors: Tabachnikov, Serge
Format: Electronic eBook
Language:Inglés
Published: Cambridge, UK ; New York : Cambridge University Press, 2005.
Series:Cambridge tracts in mathematics ; 165.
Subjects:
Projective differential geometry.
Géométrie différentielle projective.
MATHEMATICS > Geometry > Differential.
Online Access:Texto completo
Table of Contents:
  • 1. Introduction
  • 2. The Geometry of the projective line
  • 3. The Algebra of the projective line and cohomology of Diff(S1)
  • 4. Vertices of projective curves
  • 5. Projective invariants of submanifolds
  • 6. Projective structures on smooth manifolds
  • 7. Multi-dimensional Schwarzian derivatives and differential operators
  • Appendix 1. Five proofs of the Sturm theorem Appendix 2. The Language of symplectic and contact geometry
  • Appendix 3. The Language of connections
  • Appendix 4. The Language of homological algebra
  • Appendix 5. Remarkable cocycles on groups of diffeomorphisms
  • Appendix 6. The Godbillon-Vey class
  • Appendix 7. The Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry.

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