On invariant domains in certain complex homogeneous spaces

Zhou, Xiang-Yu

Annales de l'Institut Fourier, Tome 47 (1997), p. 1101-1115 / Harvested from Numdam

Résumé

Soit $K$ un groupe de Lie connexe compact. Pour un domaine $K$, $G$-invariant et relativement compact dans un espace homogène de Stein $K^{{\Bbb C}}/L^{{\Bbb C}}$, nous montrons que le groupe des automorphismes de $D$ est compact et si $K$ est semi-simple, une application holomorphe propre de $D$ est biholomorphe.

Abstract

Given a compact connected Lie group $K$. For a relatively compact $K$-invariant domain $D$ in a Stein $K^{\Bbb C}$-homogeneous space, we prove that the automorphism group of $D$ is compact and if $K$ is semisimple, a proper holomorphic self mapping of $D$ is biholomorphic.

Détail

Publié le : 1997-01-01

MR 99a:32045 | Zbl 0881.32015

DOI : https://doi.org/10.5802/aif.1593

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