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arXiv · 1512.04516

C-projective geometry

David M. J. Calderbank·Michael G. Eastwood·Vladimir S. Matveev·Katharina Neusser
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Abstract

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.

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BibTeXRIS

David M. J. Calderbank, Michael G. Eastwood, Vladimir S. Matveev, Katharina Neusser. 2015-12-14. C-projective geometry. https://doi.org/10.1090/memo/1299

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