Flat bochner curvature tensor of locally conformal kahler manifold

Abstract EN

In this paper we investigated the Bochner tensor of the class Locally Conformal Kahler manifold.

The components of the Bochner tensor of this class have been found.

We study the special class of an almost Hermatian manifold, namely R2 and we prove that, if M is Locally Conformal Kahler manifold with flat Bochner tensor, then M is a manifold of class R2 if and only if, M is a manifold of flat Ricci tensor.

Finally we proved that, if M is Locally Conformal Kahler manifold with flat Bochner and Ricci tensors, then M is Kahler manifold .