2007/11/29 by Alexander Isaev, A. V. Isaev, Isaev, A. V.
Mathematics · #32M05 #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32M05
paper · pdf · doi:10.48550/arxiv.0711.4648
6 pages
openalex publication_date 2007/11/29 · arxiv created 2008/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a characterization theorem for the unit polydisc Δn⊂\CCn in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group \hboxAut(M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) \hboxAut(M) and \hboxAut(Δn) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δn.