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 $\mathbf B$.
Citation
Akio Kodama. Satoru Shimizu. "An intrinsic characterization of the direct product of balls." J. Math. Kyoto Univ. 49 (3) 619 - 630, 2009. https://doi.org/10.1215/kjm/1260975042
Information