Some symplectic geometry on compact Kähler manifolds. I. (English) Zbl 0645.53038

Mabuchi, Toshiki

Osaka J. Math. 24, 227-252 (1987).

The aim of this paper is to define a Riemannian structure on the space of all Kähler metrics in a fixed cohomology class of a given compact Kähler manifold. This problem is analogous to the one of the establishment of a Riemannian structure in the space of all Riemannian metrics of a given compact manifold. The author deals with the natural connection of that structure and studies its geodesic and torsion and curvature tensors.

Reviewer: A.Bucki

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
58B20	Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds

Keywords:

space of Kähler metrics; natural connection; geodesic; torsion; curvature tensors