C-projective geometry
| Autor: | Calderbank, David M. J., Eastwood, Michael G., Matveev, Vladimir S., Neusser, Katharina |
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| Rok vydání: | 2015 |
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| Zdroj: | Mem. Amer. Math. Soc. 267 (2020), no. 1299, v+137 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/memo/1299 |
| Popis: | We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kaehler 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 Kaehler metrics underlying a given c-projective structure has many ramifications, which we explore in depth. As a consequence of this analysis, we prove the Yano-Obata conjecture for complete Kaehler 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. Comment: 117 pages; v2 added material on cones, local classification and outlook |
| Databáze: | arXiv |
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