Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds

Abstract

We prove two rigidity results on holomorphic isometries into homogeneous Kähler manifolds. The first shows that a Kähler-Ricci soliton induced by the homogeneous metric of the Kähler product of a special flag manifold (i.e. a flag of classical type or integral type) with a bounded homogeneous domain is trivial, i.e. Kähler-Einstein. In the second one we prove that: (i) a flat space is not relative to the Kähler product of a special flag manifold with a homogeneous bounded domain, (ii) a special flag manifold is not relative to the Kähler product of a flat space with a homogeneous bounded domain and (iii) a homogeneous bounded domain is not relative to the Kähler product of a flat space with a special flag manifold. Our theorems strongly extend the results in [4], [5], [12], [13] and [22].

14 pages

References in corpus (4)

• Kähler immersions of Kähler-Ricci solitons into definite or indefinite complex space forms
• Holomorphic isometries into homogeneous bounded domains
• Kaehler Ricci solitons induced by infinite dimensional complex space forms
• On holomorphic isometries into blow-ups of ${\mathbb{C}}^n$

Cited by in corpus (2)

• Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds
• On weak and strict relatives Kähler manifolds