On Geometry of Viasman-Gray Manifold

Abstract

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 MisViasman-Gray manifold with flat conformal curvature tensor, then M is a manifold of class R_1if and only if,Mis a manifold of flat Ricci tensor. The necessary condition that M is of zero scalar curvature tensor has been found. Finally, we proved that,ifM is VG-manifold of class W_1 and of flat Ricci tensor then MisKahler manifold.