Characterization of the unit ball in \bf Cⁿ among complex manifolds of dimension n

2004/12/28 by Alexander Isaev, Isaev, Alexander
Mathematics · #32C10 #32M05 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32C10 #msc:32M05

paper · pdf · doi:10.48550/arxiv.math/0412507

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

openalex publication_date 2004/12/28 · arxiv created 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Bⁿ⊂\CCⁿ, then M is biholomorphically equivalent to either Bⁿ or \CC\PPⁿ∖Bⁿ.

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