THE NATURAL LIFTINGS OF CONNECTIONS TO TENSOR POWERS OF THE COTANGENT BUNDLE

We reduce the problem of finding all M f(m) - natural operators B : Q -> Q (circle times(k) T*) lifting classical linear connections del on m-manifolds M into classical linear connections B-M (del) on the k th tensor power circle times(k) T* M of the cotangent bundle T* M of M to the fairly known description of all M f(m)-natural operators D : Q -> circle times(p) T* circle times circle times(q) T transforming classical linear connections del on m-manifolds M into tensor fields D-M (del) of types (q, p) on M.