Subelliptic harmonic maps, morphisms, and vector fields

Abstract

We review the salient properties of subelliptic harmonic maps and morphisms, both from a domain in ℝ^N endowed with a Hörmander system and from a strictly pseudoconvex CR manifold. We also report on several generalizations of harmonic morphisms such as heat equation morphisms from a CR manifold and b-harmonic morphisms. We discuss subelliptic harmonic vector fields within pseudohermitian geometry.