C-projective Geometry (Memoirs of the American Mathematical Society) - Softcover

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

Softcover

ISBN 10: 1470443007 ISBN 13: 9781470443009

Publisher: Amer Mathematical Society

Synopsis

The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kahler 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 Kahler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kahler 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.

Edition details

• Publisher: Amer Mathematical Society
• Language: English
• ISBN 10: 1470443007
• ISBN 13: 9781470443009
• Binding: Paperback
• Number of pages: 137