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

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


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