C-projective geometry
| Autor: | Vladimir S. Matveev, David M. J. Calderbank, Michael Eastwood, Katharina Neusser |
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| Rok vydání: | 2015 |
| Předmět: |
Mathematics - Differential Geometry
Mathematics(all) Pure mathematics Applied Mathematics General Mathematics Complex projective space Mathematical analysis Erlangen program Affine geometry math.DG Differential Geometry (math.DG) Parabolic geometry 53B10 53B35 32J27 32Q60 37J35 53A20 53C15 53C24 53C25 53C55 53D25 58J60 58J70 FOS: Mathematics Projective connection Projective differential geometry Mathematics::Differential Geometry Conformal geometry Mathematics::Symplectic Geometry Mathematics Projective geometry |
| Zdroj: | Calderbank, D M J, Eastwood, M G, Matveev, V S & Neusser, K 2020, ' C-projective geometry ', Memoirs of American Mathematical Society, vol. 267, no. 1299, pp. 0-0 . https://doi.org/10.1090/memo/1299 Calderbank, D M J, Eastwood, M G, Matveev, V S & Neusser, K 2020, ' C-projective geometry ', Memoirs of American Mathematical Society, vol. 267, no. 1299, pp. 1-150 . https://doi.org/10.1090/memo/1299 |
| DOI: | 10.48550/arxiv.1512.04516 |
| 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: | OpenAIRE |
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