The natural operators lifting connections to higher order cotangent bundles

Abstract

We prove that the problem of finding all Mf m -natural operators C: Q ↝ QT r* lifting classical linear connections ∇ on m-manifolds M into classical linear connections C M (∇) on the r-th order cotangent bundle T r*M = J r(M, ℝ)0 of M can be reduced to the well known one of describing all M f m -natural operators D: Q ↝ ⊗p T ⊗ ⊗q T* sending classical linear connections ∇ on m-manifolds M into tensor fields D M (∇) of type (p, q) on M.