An intrinsic characterization of isometric pluriharmonic immersions with codimension one (Q1299941)

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.