Geometry of Projective Tensor of Viasman-Gray Manifold

In this paper, the Vaisman-Gray manifolds with flat projective curvature tensor are investigated. It is shown that which conditions are necessary for a Vaisman-Gray manifold with flat projective curvature tensor is a nearly Kaehler (NK) manifold, a locally conformal Kahler (LCK) manifold and an Einstein manifold. Finally, The relation between certain two special classes of almost Hermitian manifold with respect to the projective tensor has been studied.