Some remarks on homogeneous Kähler manifolds

Abstract

In this paper we provide a positive answer to a conjecture due to A. J. Di Scala, A. Loi, H. Hishi (see [3, Conjecture 1]) claiming that a simply-connected homogeneous Kähler manifold M endowed with an integral Kähler form $\mu \omega$, admits a holomorphic isometric immersion in the complex projective space, for a suitable $\mu >0$. This result has two corollaries which extend to homogeneous Kähler manifolds the results obtained by the authors in [8] and in [12] for homogeneous bounded domains.

8 pages

References in corpus (3)

• Some remarks on the Gromov width of homogeneous Hodge manifolds
• The volume entropy of local Hermitian symmetric space of noncompact type
• A note on diastatic entropy and balanced metrics

Cited by in corpus (8)

• The Simanca metric admits a regular quantization
• Rawnsley's $\epsilon$-function on some Hartogs type domains over bounded symmetric domains and its applications
• Holomorphic isometries into homogeneous bounded domains
• Immersions into Sasakian space forms
• Bochner coordinates on flag manifolds
• On holomorphic isometries into blow-ups of ${\mathbb{C}}^n$
• On the diastatic entropy and C^1-rigidity of complex hyperbolic manifolds
• On weak and strict relatives Kähler manifolds