On geometry of viasman-gray manifold

Abstract EN

In this paper, we studied the geometric structure of one important class of almost Hermitian manifold which is called Viasman-Gray manifold.

This manifold is a generalization of the classes nearly Kahler manifold and the locally conformal Kahler manifold.

We provedthat, if Mis Viasman-Gray manifold with flat conformal curvature tensor, then M is a manifold of class if and only if,Mis a manifold of flat Ricci tensor.

The necessary condition that is of zero scalar curvature tensor has been found.

Finally, we proved that, ifM is VG-manifold of class and of flat Ricci tensor then Mis Kahler manifold.