One of the basic questions of CR Geometry is to ask when a smooth manifold endowed with an abstract CR structure can be realized as an embedded manifold in some formula_45. Thus not only are we embedding the manifold, but we also demand for global embedding that the map embedding the abstract manifold in formula_12 must pull back the induced CR structure of the embedded manifold( coming from the fact that it sits in formula_12) so that the pull back CR structure exactly agrees with the abstract CR structure. Thus global embedding is a two part condition. Here the question splits into two. One can ask for local embeddability or global embeddability.