C-Projective Geometry
Seiten
2021
American Mathematical Society (Verlag)
978-1-4704-4300-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4300-9 (ISBN)
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Develops in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection.
The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kahler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kahler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kahler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kahler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kahler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kahler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
David M Calderbank, University of Bath, United Kingdom Michael G. Eastwood, University of Adelaide, Australia. Vladimir S. Matveev, FSU Jena, Germany. Katharina Neusser, Charles University, Prague, The Czech Republic
| Erscheinungsdatum | 02.11.2020 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 280 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-4704-4300-7 / 1470443007 |
| ISBN-13 | 978-1-4704-4300-9 / 9781470443009 |
| Zustand | Neuware |
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