C-projective geometry

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Authors	CALDERBANK David M. J. EASTWOOD Michael G. MATVEEV Vladimir S. NEUSSER Katharina
Year of publication	2020
Type	Article in Periodical
Magazine / Source	Memoirs of the American Mathematical Society
MU Faculty or unit	Faculty of Science
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.
Related projects:	Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku