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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2005.
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| Colección: | Cambridge tracts in mathematics ;
165. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
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| Descripción Física: | 1 online resource (xi, 249 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 236-246) and index. |
| ISBN: | 9780511265785 0511265786 0521831865 9780521831864 0511263503 9780511263507 0511265069 9780511265068 9780511543142 051154314X |