Comptes Rendus
Differential Geometry
Rigidity of automorphism groups of invariant domains in certain Stein homogeneous manifolds
Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 417-420.

Given a Stein manifold XC which is homogeneous under a complex reductive Lie group GC, i.e., a complexification GC/KC 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 XC. 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.

Soit XC une variété de Stein qui est homogène sous un groupe de Lie réductif complexe GC, cést-à-dire, la complexification GC/KC 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 XC. 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.

Published online:
DOI: 10.1016/j.crma.2012.02.009

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
     author = {Fusheng Deng and Xiangyu Zhou},
     title = {Rigidity of automorphism groups of invariant domains in certain {Stein} homogeneous manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {417--420},
     publisher = {Elsevier},
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     year = {2012},
     doi = {10.1016/j.crma.2012.02.009},
     language = {en},
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DO  - 10.1016/j.crma.2012.02.009
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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.

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