Riemannian manifolds admitting pseudo W2-curvature tensor

Abstract

In this paper, we obtaine some basic geometrical properties of pseudo -curvature tensor. Then, we study pseudo ̃ symmetric ̃ manifold which recover some known results of De and Ghosh (1994). We also provide several interesting results of ̃ . Moreover, we deal with pseudo -flat perfect fluid and dust fluid spacetimes respectively. As a consequence, we obtain some important theorems. Finally, we construct a non-trivial Lorentzian metric of ̃ .