Curvature properties of projective semi-symmetric linear connections

We study a projective semi-symmetric linear connection on a differentiable manifold At endowed with a Riemannian metric g. We start with linearly independent curvature tensors R, 6 = 0,1,..., 5 and derive the tensors W for 6 = 0,1,..., 5 that, as we show, coincide with the Weyl tensor of projective curvature Wg. This confirms the well-known fact that there does not exist a generalization of the Weyl projective curvature tensor Wg.