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 by us earlier [Proc. Amer. Math. Soc. 149 (2021), pp. 4931–4941] and by Xiaoliang Cheng and Yihong Hao [Ann. Global Anal. Geom. 60 (2021), pp. 167–180].
Holomorphic isometries into homogeneous bounded domains
Loi A;Mossa R
2023-01-01
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 by us earlier [Proc. Amer. Math. Soc. 149 (2021), pp. 4931–4941] and by Xiaoliang Cheng and Yihong Hao [Ann. Global Anal. Geom. 60 (2021), pp. 167–180].File | Dimensione | Formato | |
---|---|---|---|
[23] IsomInToHBD Proc. Amer. Math. Soc. 151 (2023).pdf
Solo gestori archivio
Tipologia:
versione editoriale (VoR)
Dimensione
217 kB
Formato
Adobe PDF
|
217 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.