A parallelism for contact conformal sub-Riemannian geometry

We define a sub-conformal structure on a contact distribution over a smooth manifold and find a complete set of local invariants. This structure is shown to be a generalization of CR structures and the sub-conformal invariants reduce to the CR invariants in that case. It includes a class of almost CR structures which arise naturally as hypersurfaces of almost complex manifolds. The main difficulty of our construction is that, contrary to the integrable CR case, the appropriate bundle of coframes where the invariants are defined is not a G-structure.