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

Alexander Isaev

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

Alexander Isaev

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Abstract

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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Alexander Isaev. 2008-03-25. Characterization of the unit ball in ${\bf C}^n$ among complex manifolds of dimension $n$. https://arxiv.org/abs/math/0412507

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