Holomorphic isometries into homogeneous bounded domains
Differential Geometry
2023-12-06 v1 Complex Variables
Abstract
We prove two rigidity theorems on holomorphic isometries into homogeneous bounded domains. The first shows that a K\"ahler-Ricci soliton induced by the homogeneous metric of a homogeneous bounded domain is trivial, i.e. K\"ahler-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 K\"ahler 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.
Keywords
Cite
@article{arxiv.2205.11297,
title = {Holomorphic isometries into homogeneous bounded domains},
author = {Andrea Loi and Roberto Mossa},
journal= {arXiv preprint arXiv:2205.11297},
year = {2023}
}
Comments
11 pages. arXiv admin note: text overlap with arXiv:2003.00841