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C-Projective Geometry

David M CalderbankMichael G. EastwoodVladimir S. MatveevKatharina Neusser

出版	American Mathematical Society, 2021-02-10
主題	Mathematics / General
ISBN	14704430079781470443009
URL	http://books.google.com.hk/books?id=cnUjEAAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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 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 the authors explore in depth. As a consequence of this analysis, they 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.