C-projective geometry

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

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)1-150
JournalMemoirs of American Mathematical Society
Volume267
Issue number1299
Early online date4 Jan 2021
DOIs
Publication statusE-pub ahead of print - 4 Jan 2021

Keywords

  • math.DG
  • 53B10, 53B35, 32J27, 32Q60, 37J35, 53A20, 53C15, 53C24, 53C25, 53C55, 53D25, 58J60, 58J70

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