A Lorentz form associated to contact sub-conformal and CR manifolds

Abstract

We construct a bilinear form associated to a sub-conformal structure on a manifold M. In the case the sub-conformal structure corresponds to a partially-integrable CR structure we obtain a conformal Lorentz structure which coincides with Fefferman's construction on a circle bundle over M. The main contribution is the use of invariant forms with values in a vector space instead of the full information contained in the Cartan connection in order to simplify the construction.