Return to home page
Searching: Muskingum library catalog
Record 50 of 61
  Previous Record Previous Item Next Item Next Record
  Reviews, Summaries, etc...
EBOOK
Author Ovsienko, Valentin.
Title Projective differential geometry old and new : from the Schwarzian derivative to the cohomology of diffeomorphism groups / V. Ovsienko, S. Tabachnikov.
Imprint Cambridge, UK ; New York : Cambridge University Press, 2005.

Series Cambridge tracts in mathematics ; 165.
Cambridge tracts in mathematics ; 165.
Subject Projective differential geometry.
Alt Name Tabachnikov, Serge.
Series Cambridge tracts in mathematics ; 165.
Cambridge tracts in mathematics ; 165.
Subject Projective differential geometry.
Alt Name Tabachnikov, Serge.
Description 1 online resource (xi, 249 pages) : illustrations.
Bibliography Note Includes bibliographical references (pages 236-246) and index.
Note Print version record.
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.
Summary 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 proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
ISBN 9780511265785 (electronic bk.)
0511265786 (electronic bk.)
0521831865 (hardback)
9780521831864 (hardback)
0511263503 (ebook)
9780511263507 (ebook)
0511265069 (electronic bk.)
9780511265068 (electronic bk.)
9780511543142
051154314X
OCLC # 82365929
Additional Format Print version: Ovsienko, Valentin. Projective differential geometry old and new. Cambridge, UK ; New York : Cambridge University Press, 2005 0521831865 9780521831864 (DLC) 2004045919 (OCoLC)54953058.