Geodesic
Characterization of $\mathbb C^n$ by Its Automorphism Group
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 110-113.

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We show that if the group of holomorphic automorphisms of a connected Stein manifold $M$ is isomorphic to that of $\mathbb C^n$ as a topological group equipped with the compact-open topology, then $M$ is biholomorphically equivalent to $\mathbb C^n$. 
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     title = {Characterization of $\mathbb C^n$ by {Its} {Automorphism} {Group}},
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A. V. Isaev. Characterization of $\mathbb C^n$ by Its Automorphism Group. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 110-113. http://geodesic.mathdoc.fr/item/TRSPY_2001_235_a7/

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