Characterization of the unit ball in ${\bf C}^n$ among complex manifolds of dimension $n$

Details Characterization of the unit ball in ${\bf C}^n$ among complex manifolds of dimension $n$ Characterization of the unit ball in ${\bf C}^n$ among complex manifolds of dimension $n$

2004-12-28

arxiv.org/abs/math/0412507v2

Mathematics

Complex Variables

J. Geometric Analysis 14(2004), 697-700; erratum, to appear in J. Geometric Analysis 18(2008), no. 3

Scientific paper

We show that if the group of holomorphic automorphisms of a connected complex
manifold $M$ of dimension $n$ is isomorphic as a topological group equipped
with the compact-open topology to the automorphism group of the unit ball
$B^n\subset\CC^n$, then $M$ is biholomorphically equivalent to either $B^n$ or
$\CC\PP^n\setminus\bar{B^n}$.

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