An intrinsic characterization of the direct product of balls
Akio Kodama and Satoru Shimizu
Source: J. Math. Kyoto Univ.
Volume 49, Number 3
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.kjm/1260975042
Mathematical Reviews number (MathSciNet): MR2583605
Zentralblatt MATH identifier: 05696850