Pseudo curvature tensor ̃ on a Riemannian manifold

Abstract

In this paper we introduce a new curvature tensor named as Pseudo curvature tensor ̃. Some algebraic properties of Pseudo curvature tensor ̃ are obtained. Further Quadratic killing tensor ̃ and Quadratic conformal killing tensor ̃ are considered with respect to Pseudo curvature tensor ̃. Finally it is proved that Pseudo curvature tensor ̃ is conservative if the scalar curvature tensor is constant under the certain condition.