Curvature properties of projective semi-symmetric linear connections

. We study a projective semi-symmetric linear connection on a differentiable manifold M endowed with a Riemannian metric g . We start with linearly independent curvature tensors R θ , θ = 0 , 1 ,..., 5 and derive the tensors W θ for θ = 0 , 1 ,..., 5 that, as we show, coincide with the Weyl tensor of projective curvature W g . This confirms the well-known fact that there does not exist a generalization of the Weyl projective curvature tensor W g .