Kähler Immersions of Homogeneous Kähler Manifolds into Complex Space Forms

Abstract

In this paper we study the homogeneous Kähler manifolds (h.K.m.) which can be Kähler immersed into finite or infinite dimensional complex space forms. On the one hand we completely classify the h.K.m. which can be Kähler immersed into a finite or infinite dimensional complex Euclidean or hyperbolic space. On the other hand, we extend known results about Kähler immersions into the finite dimensional complex projective space to the infinite dimensional setting.