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2019 A group-theoretic characterization of the Fock-Bargmann-Hartogs domains
Akio Kodama
Tohoku Math. J. (2) 71(4): 559-580 (2019). DOI: 10.2748/tmj/1576724794

Abstract

Let $M$ be a connected Stein manifold of dimension $N$ and let $D$ be a Fock-Bargmann-Hartogs domain in $\mathbb{C}^N$. Let $\mathrm{Aut}(M)$ and $\mathrm{Aut}(D)$ denote the groups of all biholomorphic automorphisms of $M$ and $D$, respectively, equipped with the compact-open topology. Note that $\mathrm{Aut}(M)$ cannot have the structure of a Lie group, in general; while it is known that $\mathrm{Aut}(D)$ has the structure of a connected Lie group. In this paper, we show that if the identity component of $\mathrm{Aut}(M)$ is isomorphic to $\mathrm{Aut}(D)$ as topological groups, then $M$ is biholomorphically equivalent to $D$. As a consequence of this, we obtain a fundamental result on the topological group structure of $\mathrm{Aut}(D)$.

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Akio Kodama. "A group-theoretic characterization of the Fock-Bargmann-Hartogs domains." Tohoku Math. J. (2) 71 (4) 559 - 580, 2019. https://doi.org/10.2748/tmj/1576724794

Information

Published: 2019
First available in Project Euclid: 19 December 2019

zbMATH: 07199980
MathSciNet: MR4043926
Digital Object Identifier: 10.2748/tmj/1576724794

Subjects:
Primary: 32A07
Secondary: 32M05

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 4 • 2019
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