Deformation of Kahler metrics to Kahler-Einstein metrics on compact Kahler manifolds
Metric deformation methods are used to give a more geometric proof of the well known Calabi conjectures of Kahler geometry. More precisely, it is proven that given any closed (1,1) form on a compact Kahler manifold M, which represents the first Chern class of M, one can deform the initial metric by certain Hamilton's type equation to the limit Kahler metric which has the given (1,1) form as its Ricci form. In case the first Chern class of M is negative, the appropriate initial metric can also be deformed along the parabolic Einstein equation to the unique Kahler-Einstein metric. The method involves the study of the a priori estimates and the asymptotic behavior of the solutions to the evolution equations. It is remarked that the above Calabi conjectures were first proved by Yau in 1976 by solving certain complex Monge-Ampere equations.
- Research Organization:
- Princeton Univ., NJ (USA)
- OSTI ID:
- 5552034
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
New spin(7) holonomy metrics admitting G{sub 2} holonomy reductions and M-theory/type-IIA dualities
Janus and -fold solutions from Sasaki-Einstein manifolds