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A REMARK ON THE N-INVARIANT GEOMETRY OF BOUNDED HOMOGENEOUS DOMAINS
Published online by Cambridge University Press: 23 May 2024
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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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal