Moduli space of isometric pluriharmonic immersions of Kähler manifolds into indefinite Euclidean spaces (Q1358965)

It has been a fundamental problem in the theory of minimal surfaces to determine the moduli spaces of isometric minimal immersions. An answer to this problem was given by \textit{E. Calabi} [Quelques applications de l'analyse complex aux surfaces d'aire minima, Topics in complex manifolds (by Rossi, H.), Univ. Montreal, 59-81 (1968)], and recently it is generalized to higher dimensional cases by the present author, \textit{H. Furuhata} [Bull. Lond. Math. Soc. 26, No. 5, 487-496 (1994; Zbl 0820.53006)]. The purpose of this paper is to prove the counterpart of this construction in the case that the ambient space is an indefinite Euclidean space. Namely, a parametrization of the moduli space of isometric pluriharmonic immersions of a simply connected Kähler manifold into an indefinite real Euclidean space in terms of certain matrices, which are in fact determined by a full isometric holomorphic immersion, is constructed. The key ingredient of this construction is the pluriharmonicity of these immersions, which eventually enables to classify them in a similar fashion as in the case of minimal surfaces. Some examples of the pluriharmonic immersions are also given.