Bochner-flat Kähler manifolds and Riemannian compatibility of the Ricci tensor

Mileva Prvanović

In this paper we investigate Riemannian compatibility of Ricci tensor of a Bochner-flat Kähler manifold, and specially of a such manifolds which is of quasi-constant holomorphic sectional curvature. Also, we extend our consideration to manifolds without Bochner-flat condition. In all cases we found necessary and sufficient conditions on the Ricci tensor of considered manifolds to be Riemannian compatible.