Abstract. Let p C : C = CN → N be the bundle of linear connections on a smooth manifold N and let p M : M → N be the bundle of pseudo-Riemannian metrics of a given signature (n + , n − ), n + + n − = n = dim N on N. The structure of the first-order Lagrangians defined on the bundle M × N C → N that are invariant under the natural action of the diffeomorphisms of N, is determined
