Kaehler immersions of homogeneous Kaehler manifolds into complex space forms

TL;DR

This paper classifies homogeneous Kaehler manifolds that can be immersed into complex space forms, extending known finite-dimensional results to infinite-dimensional settings and providing a comprehensive understanding of their immersion properties.

Contribution

It completely classifies homogeneous Kaehler manifolds immersible into complex space forms, including infinite-dimensional cases, extending previous finite-dimensional results.

Findings

Classification of h.K.m. immersible into complex Euclidean and hyperbolic spaces

Extension of Kaehler immersion results to infinite-dimensional spaces

Identification of conditions for immersibility into complex projective spaces

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 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. Moreover, we extend known results about Kaehler immersions into the finite dimensional complex projective space to the infinite dimensional setting.