Twistor cr manifolds and three-dimensional conformal geometry

A CR (i.e. partially complex) 5-manifold is contructed as a sphere bundle over an arbitrary 3-manifold with conformal metric. This so-called twistor CR manifold is show to capture completely the original geometry, and necessary and sufficient conditions are given for an abstract CR manifold to arise via the construction. The above correspondence is then used to prove that a twistor CR manifold is locally imbeddable as a real hypersurface in C³ only if it is real-analytic with respect to a suitable atlas.