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 ℝⁿ in terms of an integral representation of Weierstraß type. Restricting to the case of immersions in ℝ⁴, we study harmonicity conditions for such immersions and give a complete classification of CR-pluriharmonic immersions.