CLASSIFICATION OF FLAT PSEUDO-KAHLER SUBMANIFOLDS IN COMPLEX PSEUDO-EUCLIDEAN SPACES

Calabi [1] gave a classification of Kahler imbeddings of complete, simply-connected definite complex space forms into complete, simply-connected definite complex space forms. The local version of Calabi's result was obtained by Nakagawa and Ogiue in [5]. In contrast, no classification results were known for pseudo-Kahler immersions between indefinite complex space forms. In this article, we initiate the study of the classification problem on pseudo-Kahler immersions between indefinite complex space forms. As a consequence, three classification theorems for pseudo-Kahler immersions between flat indefinite complex space forms are obtained.