Hokkaido Mathematical Journal

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

Andrea ALTOMANI and 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 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.

Article information

Source
Hokkaido Math. J., Volume 42, Number 2 (2013), 209-238.

Dates
First available in Project Euclid: 3 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1372859585

Digital Object Identifier
doi:10.14492/hokmj/1372859585

Mathematical Reviews number (MathSciNet)
MR3112456

Zentralblatt MATH identifier
1277.53052

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space 32V10: CR functions 53D10: Contact manifolds, general

Keywords
Isometric immersions CR pluriharmonic immersions strongly pseudoconvex CR manifolds

Citation

ALTOMANI, Andrea; LAWN, Marie-Amélie. Isometric and CR pluriharmonic immersions of three dimensional CR manifolds in Euclidean spaces. Hokkaido Math. J. 42 (2013), no. 2, 209--238. doi:10.14492/hokmj/1372859585. https://projecteuclid.org/euclid.hokmj/1372859585


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