关于有界同质域 n 不变几何的评论

IF 0.8 2区数学 Q2 MATHEMATICS Nagoya Mathematical Journal Pub Date : 2024-05-23 DOI:10.1017/nmj.2024.12

L. Geatti, A. Iannuzzi

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引用次数: 0

摘要

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

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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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.

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