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

Dajczer, Marcos; Rodríguez, Lucio

Mat. Contemp. 4, 95-98 (1993).

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.

MSC:

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

Keywords:

holomorphy; index of relative nullity; isometric immersions of connected Kähler manifolds; non-flat complex space forms