Kähler immersions of homogeneous Kähler manifolds into complex space forms

Abstract

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