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A REMARK ON THE N-INVARIANT GEOMETRY OF BOUNDED HOMOGENEOUS DOMAINS
- Part of
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- Journal:
- Nagoya Mathematical Journal / Volume 256 / December 2024
- Published online by Cambridge University Press:
- 23 May 2024, pp. 928-937
- Print publication:
- December 2024
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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.
