On isometric immersions into complex space forms. (English) Zbl 0852.53044

The main purpose of this paper is to study isometric immersions of connected Kähler manifolds into non-flat complex space forms. The question of when such an isometric immersion is holomorphic is an interesting problem. This question has been successfully studied in the more general setting of harmonic maps by several authors, where they require the manifolds to be compact. In our case, a positive result is obtained under local conditions only.


53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables