C-projective geometry

• Autoři: CALDERBANK David M. J.; EASTWOOD Michael G.; MATVEEV Vladimir S.; NEUSSER Katharina
• Rok publikování: 2020
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Memoirs of the American Mathematical Society
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1090/memo/1299
• Doi: http://dx.doi.org/10.1090/memo/1299
• Klíčová slova: c-projective geometry; tractor bundle; metrizable space
• Popis: 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.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku