C-projective geometry
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Memoirs of the American Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1090/memo/1299 |
| Doi | http://dx.doi.org/10.1090/memo/1299 |
| Keywords | c-projective geometry; tractor bundle; metrizable space |
| Description | We develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler 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 Kähler 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 Kähler 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. |
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