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

Alexander Isaev

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

Complex Variables 2008-03-25 v2

Authors: Alexander Isaev

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 $\CC\PP^n\setminus\bar{B^n}$ .

Keywords

complex manifolds unit ball holomorphic automorphisms biholomorphic equivalence compact-open topology

Cite

@article{arxiv.math/0412507,
  title  = {Characterization of the unit ball in ${\bf C}^n$ among complex manifolds of dimension $n$},
  author = {Alexander Isaev},
  journal= {arXiv preprint arXiv:math/0412507},
  year   = {2008}
}

Comments

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

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

Abstract

Keywords

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