Hokkaido Mathematical Journal

ALTOMANI Andrea, LAWN Marie-Amélie,

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

Hokkaido Mathematical Journal, 42 (2013) pp.209-238

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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.

MSC(Primary)53C42
MSC(Secondary)53A07, 32V10, 53D10
Uncontrolled KeywordsIsometric immersions, CR pluriharmonic immersions, strongly pseudoconvex CR manifolds