### An intrinsic characterization of the direct product of balls

Akio Kodama and Satoru Shimizu
Source: J. Math. Kyoto Univ. Volume 49, Number 3 (2009), 619-630.

#### Abstract

In this paper, we give a characterization of the direct product of balls by its holomorphic automorphism group. Using a result on the standardization of certain compact group actions on complex manifolds, we show that, for a connected Stein manifold $M$ of dimension $n$, if its holomorphic automorphism group contains a topological subgroup that is isomorphic to the holomorphic automorphism group of the direct product $\mathbf B$ of balls in $\mathbf C^n$, then $M$ itself is biholomorphically equivalent to $\mathbf B$.

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Primary Subjects: 32M05
Secondary Subjects: 32A07