CURVATURE COPIES AND THE UNIQUENESS OF BIANCHI-TYPE EQUATIONS - THE SYMMETRICAL CONNECTION CASE

It is shown, in general circumstances in a four-dimensional spacetime. that (i) the symmetric metric connection of a Riemann tensor cannot b e a curvature copy of a symmetric non-metric connection, (ii) the only Bianchi-type equation (in a symmetric connection) obeyed by a Riemann tensor is its own Bianchi equation. Further, these results for Rieman n tensors (of metric connections) are generalized naturally to curvatu re tensors of Weyl connections.