Invariant bidifferential operators on tensor densities over a contact manifold

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.