Invariant Bidifferential Operators on Tensor Densities over a Contact Manifold

Abstract

The spaces of tensor densities over a manifold M are modules over the Lie algebra Vect(M) of vector fields over the manifold. When M is a contact manifold, one can consider the algebra C(M) of vector fields which preserves the contact structure. If the manifold is endowed with a contact projective structure, there is an embedding of the linear symplectic algebra sp(2n+2, ℝ) in C(M). In this Letter, we determine the C(M)- and the sp(2n+2, ℝ)-invariant bidifferential operators on tensor densities.