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

By:

Ovsienko, V

Contributor(s):

Tabachnikov, S [Co-author]

Series: Cambridge tracts in mathematics, no. 165Publication details: Cambridge University Press, 2005. Cambridge:Description: xi, 249p.; hbk; 24cmISBN:

9780511543142

Subject(s):

DDC classification:

516.36 OVS

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. https://www.cambridge.org/core/books/projective-differential-geometry-old-and-new/25BE15C0126E8A1D8F5EC90827C7704B#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	516.36 OVS (Browse shelf(Opens below))	1	Available		031760

Includes index and references

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.

https://www.cambridge.org/core/books/projective-differential-geometry-old-and-new/25BE15C0126E8A1D8F5EC90827C7704B#fndtn-information

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