On riemannian manifolds admitting w₂-curvature tensor

The object of this paper is to study the properties of flat spacetimes under some conditions regarding the W₂-curvature tensor. In the first section, several results are obtained on the geometrical symmetries of this curvature tensor. It is shown that in a spacetime with W₂-curvature tensor filled with a perfect fluid, the energy momentum tensor satisfying the Einstein's equations with a cosmological constant is a quadratic conformal Killing tensor. It is also proved that a necessary and sufficient condition for the energy momentum tensor to be a quadratic Killing tensor is that the scalar curvature of this space must be constant. In a radiative perfect fluid, it is shown that the sectional curvature is constant.