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

DOI10.14492/HOKMJ/1372859585zbMATH Open1277.53052arXiv1106.2962OpenAlexW1991373037MaRDI QIDQ354024

Marie-Amélie Lawn, Andrea Altomani

Publication date: 17 July 2013

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1106.2962

zbMATH Keywords

isometric immersionsCR pluriharmonic immersionsstrongly pseudoconvex CR manifolds

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Contact manifolds (general theory) (53D10) CR functions (32V10)

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