  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.
