A group-theoretic characterization of the direct product of a ball and a Euclidean space

Jisoo Byun; Akio Kodama; Satoru Shimizu

doi:10.1515/FORUM.2006.050

A group-theoretic characterization of the direct product of a ball and a Euclidean space

Jisoo Byun, Akio Kodama, Satoru Shimizu

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Let M be a connected Stein manifold of dimension n. We show that if the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of B^k × ℂ^n-k as topological group, then M itself is biholomorphically equivalent to B^k × ℂ^n-k, where B^k denotes the open unit ball in ℂ^k.

Original language	English
Pages (from-to)	983-1009
Number of pages	27
Journal	Forum Mathematicum
Volume	18
Issue number	6
DOIs	https://doi.org/10.1515/FORUM.2006.050
Publication status	Published - 2006 Nov 20

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1515/FORUM.2006.050

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abstract = "Let M be a connected Stein manifold of dimension n. We show that if the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of Bk × ℂn-k as topological group, then M itself is biholomorphically equivalent to Bk × ℂn-k, where Bk denotes the open unit ball in ℂk.",

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AB - Let M be a connected Stein manifold of dimension n. We show that if the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of Bk × ℂn-k as topological group, then M itself is biholomorphically equivalent to Bk × ℂn-k, where Bk denotes the open unit ball in ℂk.

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A group-theoretic characterization of the direct product of a ball and a Euclidean space

Abstract

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