## Abstract

In this paper, we prove that the holomorphic automorphism groups of the spaces C^{k} × (C*)^{n-k} and (C^{k} - {0}) × (C*)^{n-k} are not isomorphic as topological groups. By making use of this fact, we establish the following characterization of the space C^{k} × (C*)^{n-k}: Let M be a connected complex manifold of dimension n that is holomorphically separable and admits a smooth envelope of holomorphy. Assume that the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of C^{k} × (C*)^{n-k} as topological groups. Then M itself is biholomorphically equivalent to C^{k} × (C*)^{n-k}. This was first proved by us in [5] under the stronger assumption that M is a Stein manifold.

Original language | English |
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Pages (from-to) | 643-663 |

Number of pages | 21 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 58 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 Jul |

## Keywords

- Holomorphic automorphism groups
- Holomorphic equivalences
- Torus actions

## ASJC Scopus subject areas

- Mathematics(all)