A PARALLELISM FOR CONTACT CONFORMAL SUB-RIEMANNIAN GEOMETRY

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