Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold
Let be a differentiable manifold with a pseudo-Riemannian metric and a linear symmetric connection . We classify all natural (in the sense of [KMS]) 0-order vector fields and 2-vector fields on generated by and . We get that all natural vector fields are of the form where is the vertical lift of , is the horizontal lift of with respect to , and are smooth real functions defined on . All natural 2-vector fields are of the form where , are smooth real functions defined...