Holomorphic isometries into homogeneous bounded domains

Abstract

We prove two rigidity theorems on holomorphic isometries into homogeneous bounded domains. The first shows that a Kähler-Ricci soliton induced by the homogeneous metric of a homogeneous bounded domain is trivial, i.e. Kähler-Einstein. In the second one we prove that a homogeneous bounded domain and the flat (definite or indefinite) complex Euclidean space are not relatives, i.e. they do not share a common Kähler submanifold (of positive dimension). Our theorems extend the results proved in [A. Loi, R. Mossa, Proc. Amer. Math. Soc. 149 (2021), no. 11, 4931-4941] and [X. Cheng, Y. Hao, Ann. Global Anal. Geom. 60 (2021), no. 1, 167-180] respectively.

11 pages. arXiv admin note: text overlap with arXiv:2003.00841

References in corpus (1)

• Kaehler Ricci solitons induced by infinite dimensional complex space forms

Cited by in corpus (4)

• Umehara algebra and complex submanifolds of indefinite complex space forms
• On local holomorphic maps between Kähler manifolds preserving $(p,p)$-forms
• Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds
• On weak and strict relatives Kähler manifolds