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arXiv · 1106.2962

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

Andrea Altomani·Marie-Amélie Lawn
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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.

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Andrea Altomani, Marie-Amélie Lawn. 2012-02-19. Isometric and CR pluriharmonic immersions of three dimensional CR manifolds in Euclidean spaces. https://arxiv.org/abs/1106.2962

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