Isometric and CR pluriharmonic immersions of three dimensional CR manifolds in Euclidean spaces

Abstract

Using a bigraded differential complex depending on the CR and pseudohermitian structure, we give a characterization of three-dimensional strongly pseudoconvex pseudo-hermitian CR-manifolds isometrically immersed in Euclidean space ${\mathbb{R}}^n$ in terms of an integral representation of Weierstrass type. Restricting to the case of immersions in ${\mathbb{R}}^4$, we study harmonicity conditions for such immersions and give a complete classification of CR-pluriharmonic immersions.

arXiv comment24 pages; v2: final accepted version