On invariant domains in certain complex homogeneous spaces

Zhou, Xiang-Yu

Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1101-1115.

Soit $K$ un groupe de Lie connexe compact. Pour un domaine $K$, $G$-invariant et relativement compact dans un espace homogène de Stein $K^{ℂ}/L^{ℂ}$, 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.

Given a compact connected Lie group $K$. For a relatively compact $K$-invariant domain $D$ in a Stein $K^{ℂ}$-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.

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