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

Published by De Gruyter February 27, 2007

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

Jisoo Byun , Akio Kodama and Satoru Shimizu

From the journal Forum Mathematicum

https://doi.org/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 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.

(Communicated by Junjiro Noguchi)

Received: 2004-10-06

Accepted: 2005-06-19

Published Online: 2007-02-27

Published in Print: 2006-11-20

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

Abstract

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