C-Projective Geometry

The authors develop the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. They realize 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 the existence of two or more Kahler metrics underlying a given c-projective structure has many ramifications. They prove the Yano–Obata Conjecture for complete Kahler manifolds, which states that 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.

Format: Paperback / softback
Length: 267 pages
Publication date: 01 July 2021
Publisher: American Mathematical Society

The authors delve into the intricate theory of (almost) c-projective geometry, a remarkable adaptation of projective differential geometry tailored for (almost) complex manifolds. They perceive it as a branch of parabolic geometry and elucidate the associated Cartan or tractor connection. A Kahler manifold serves as the foundation for a c-projective structure, making it a subject of profound exploration. The presence of two or more Kahler metrics underlying a given c-projective structure yields a multitude of consequences, which the authors meticulously examine. Through this comprehensive analysis, they establish the Yano–Obata Conjecture for complete Kahler manifolds. This conjecture asserts that if a manifold possesses a one-parameter group of c-projective transformations that are not affine, it is indeed complex projective space, adorned with a multiple of the Fubini-Study metric.

The authors meticulously develop the theory of (almost) c-projective geometry, a profound analog of projective differential geometry tailored for (almost) complex manifolds. They perceive it as a branch of parabolic geometry and elucidate the associated Cartan or tractor connection. A Kahler manifold serves as the foundation for a c-projective structure, making it a subject of profound exploration. The presence of two or more Kahler metrics underlying a given c-projective structure yields a multitude of consequences, which the authors meticulously examine. Through this comprehensive analysis, they establish the Yano–Obata Conjecture for complete Kahler manifolds. This conjecture asserts that if a manifold possesses a one-parameter group of c-projective transformations that are not affine, it is indeed complex projective space, adorned with a multiple of the Fubini-Study metric.

Weight: 280g
ISBN-13: 9781470443009