Geometry of Projective Tensor of Viasman-Gray Manifold
Habeeb M. Abood *
Department of Mathematics, College of Education for Pure Sciences, Basra University, Basra, Iraq.
Hadeel G. Abd Ali
Department of Mathematics, College of Education for Pure Sciences, Basra University, Basra, Iraq.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Almost Hermitian manifold, Viasman-Gray manifold, projective tensor