A REMARK ON THE N-INVARIANT GEOMETRY OF BOUNDED HOMOGENEOUS DOMAINS

Pub Date : 2024-05-23 DOI:10.1017/nmj.2024.12

L. Geatti, A. Iannuzzi

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Abstract

Let

$\mathbf {D}$

be a bounded homogeneous domain in

${\mathbb {C}}^n$

. In this note, we give a characterization of the Stein domains in

$\mathbf {D}$

which are invariant under a maximal unipotent subgroup N of

$Aut(\mathbf {D})$

. We also exhibit an N-invariant potential of the Bergman metric of

$\mathbf {D}$

, expressed in a Lie theoretical fashion. These results extend the ones previously obtained by the authors in the symmetric case.

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关于有界同质域 n 不变几何的评论

让 $\mathbf {D}$ 是 ${mathbb {C}}^n$ 中的有界同质域。在本注释中，我们给出了$\mathbf {D}$中在$Aut(\mathbf {D})$的最大单能子群N下不变的斯坦因域的特征。我们还展示了$\mathbf {D}$ 的伯格曼度量的N不变势，并以李理论的方式表达出来。这些结果扩展了作者之前在对称情况下获得的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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