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An intrinsic characterization of isometric pluriharmonic immersions with codimension one. (English) Zbl 0931.53029

An isometric immersion of a Kähler manifold into semi-Euclidean space is said to be pluriharmonic if the \((1,1)\)-component of its complexified second fundamental form vanishes identically. The class of such immersions can be regarded as a generalization of minimal surfaces in Euclidean space. In this paper, the author gives a necessary and sufficient condition for a Kähler manifold \(M^{2m}\) to have isometric pluriharmonic immersions into semi-Euclidean space \(\mathbb R^{2m+1}_N\) \((N=0\) or \(1)\), generalizing the Ricci-Curbastro theorem.
Reviewer: W.Mozgawa (Lublin)

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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