Characterization of ${\bf C}^n$ by its automorphism group

Details Characterization of ${\bf C}^n$ by its automorphism group Characterization of ${\bf C}^n$ by its automorphism group

2000-08-25

arxiv.org/abs/math/0008193v1

Mathematics

Complex Variables

to appear in Proc. Steklov Inst. math

Scientific paper

We show that if the group of holomorphic automorphisms of a connected Stein
manifold $M$ is isomorphic to that of ${\bf C}^n$ as a topological group
equipped with the compact-open topology, then $M$ is biholomorphically
equivalent to ${\bf C}^n$.

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