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 236246) 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. Multidimensional 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 GodbillonVey class  Appendix 7. The AdlerGelfandDickey bracket and infinitedimensional 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. Onedimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical fourvertex 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 multidimensional 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. 
