Space-time Admitting W4-Curvature Tensor

Abstract

In this paper, we have studied space-time with W4-curvature tensor and proved that a 4-dimensional relativistic W4-flat space-time satisfying Einstein's field equation with cosmological constant, the energy-momentum tensor is covariant constant. It is also observed that in a 4-dimensional relativistic space-time M has conservative W4-curvature tensor if and only if the energy momentum tensor is Codazzi tensor provided that the scalar curvature is constant in both the cases.