Curved Versions of the Ovsienko-Redou Operators

Abstract

We construct a family of conformally covariant bidifferential operators on pseudo-Riemannian manifolds. Our construction is analogous to the construction of Graham-Jenne-Mason-Sparling of conformally covariant differential operators via tangential powers of the Laplacian in the Fefferman-Graham ambient space. In fact, we completely classify the tangential bidifferential operators on the ambient space, which are expressed purely in terms of the ambient Laplacian. This gives a curved analogue of the classification, due to Ovsienko-Redou and Clerc, of conformally invariant bidifferential operators on the sphere. As an application, we construct a large class of formally self-adjoint conformally invariant differential operators.