Rigidity of automorphism groups of invariant domains in certain Stein homogeneous manifolds

Fusheng Deng; Xiangyu Zhou

doi:10.1016/j.crma.2012.02.009

Differential Geometry

Rigidity of automorphism groups of invariant domains in certain Stein homogeneous manifolds
[Rigidité de groupe dʼautomorphismes dʼun domaine invariant dans les variétés de Stein homogène]

Présenté par : Jean-Pierre Demailly

Fusheng Deng ¹ ; Xiangyu Zhou ²

¹ School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China
² Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China

Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 417-420.

Résumé
Abstract

Soit $X_{C}$ une variété de Stein qui est homogène sous un groupe de Lie réductif complexe $G_{C}$ , cést-à-dire, la complexification $G_{C} / K_{C}$ dʼun espace homogène compact $G / K$ . Soit D un domaine relativement compact qui est invariant par rapport à la forme compacte G de groupe de Lie réductif complexe dans $X_{C}$ . On trouve une relation entre le groupe dʼautomorphismes du domaine invariant D et le groupe dʼisométrie de lʼespace homogène compact $G / K$ . Si lʼespace homogène compact $G / K$ est isotropie irréductible, on obtient une propriété de rigidité du groupe dʼautomorphismes.

Given a Stein manifold $X_{C}$ which is homogeneous under a complex reductive Lie group $G_{C}$ , i.e., a complexification $G_{C} / K_{C}$ of a compact homogeneous space $G / K$ . Consider a relatively compact domain D which is invariant w.r.t. the compact real form G of the complex reductive Lie group in the Stein manifold $X_{C}$ . We find a relation between the automorphism group of the invariant domain D and isometric group of the compact homogeneous space $G / K$ . When the compact homogeneous space $G / K$ is isotropy irreducible, or even more general, we obtain a rigidity property of the automorphism groups.

Reçu le : 2010-10-18
Accepté le : 2012-02-23
Publié le : 2012-04-01

DOI : 10.1016/j.crma.2012.02.009

Affiliations des auteurs :

Fusheng Deng ¹ ; Xiangyu Zhou ²

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     title = {Rigidity of automorphism groups of invariant domains in certain {Stein} homogeneous manifolds},
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Fusheng Deng; Xiangyu Zhou. Rigidity of automorphism groups of invariant domains in certain Stein homogeneous manifolds. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 417-420. doi : 10.1016/j.crma.2012.02.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.02.009/

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