The unit sphere and CR geometry

Abstract

CR geometry considers the interplay between real and complex spaces. The name itself has an interesting history, which we do not discuss here, other than to say that CR stands both for Cauchy-Riemann and for Complex-Real. See [DT] for a survey of CR Geometry and its connections with other branches of mathematics. See [J] for a good exposition of the theory of CR structures, and see [BER] for a definitive treatment of CR mappings.