C-projective geometry

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

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2 Citations (SciVal)
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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.

Original languageEnglish
Pages (from-to)1-150
Number of pages150
JournalMemoirs of American Mathematical Society
Issue number1299
Publication statusPublished - 31 Dec 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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