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

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

2011-06-15

arxiv.org/abs/1106.2962v2

Mathematics

Differential Geometry

24 pages; v2: final accepted version

Scientific paper

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.

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