Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups: 165 (Cambridge Tracts in Mathematics, Series Number 165) - Hardcover

Ovsienko, V.; Tabachnikov, S.

Hardcover

ISBN 10: 0521831865 ISBN 13: 9780521831864

Publisher: Cambridge University Press, 2005

Synopsis

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.

About this title

Review

'... this is an introduction to global projective differential geometry offering felicitous choice of topics, leading from classical projective differential geometry to current fields of research in mathematics and mathematical physics. The reader is guided from simple facts concerning curves and derivatives to more involved problems and methods through a world of inspiring ideas, delivering insights in deep relations. Historical comments as well as stimulating exercises occur frequently throughout the text, making it suitable for teachings.' Zentralblatt MATH

Book Description

Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. This 2005 book provides a rapid route for graduate students and researchers to the frontiers of contemporary research in this evergreen subject. Exercises play a prominent role: historical and cultural comments relate the basic notions to a broader context.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2005
• ISBN 10: 0521831865
• ISBN 13: 9780521831864
• Binding: Hardcover
• Language: English
• Number of pages: 262