In this paper we study the homogeneous Ka ̈hler manifolds (h.K.m.) which can be K ̈ahler immersed into finite or infinite dimensional complex space forms. On the one hand we completely classify the h.K.m. which can be Ka ̈hler immersed into a finite or infinite dimensional complex Euclidean or hyperbolic space. On the other hand, we extend known results about Ka ̈hler immersions into the finite dimensional complex projective space to the infinite dimensional setting.
Kaehler Immersions of Homogeneous Kaehler Manifolds into Complex Space Forms
LOI, ANDREA;
2012-01-01
Abstract
In this paper we study the homogeneous Ka ̈hler manifolds (h.K.m.) which can be K ̈ahler immersed into finite or infinite dimensional complex space forms. On the one hand we completely classify the h.K.m. which can be Ka ̈hler immersed into a finite or infinite dimensional complex Euclidean or hyperbolic space. On the other hand, we extend known results about Ka ̈hler immersions into the finite dimensional complex projective space to the infinite dimensional setting.
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