CR Embeddings, Chains, and the Fefferman Bundle

Abstract

In this paper it is shown that a CR embedding from one strictly pseudoconvex hypersurface into another (of strictly larger dimension) sends chains on the source to chains on the target if and only if the embedding has a lift to a conformal isometry of the associated Fefferman bundles with vanishing pseudo-Riemannian second fundamental form. When the target is a sphere these conditions simplify nicely.