2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157351We 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 $B^n\subset\CC^n$, then $M$ is biholomorphically equivalent to either $B^n$ or $\CC\PP^n\setminus\bar{B^n}$.J. Geometric Analysis 14(2004), 697-700; erratum, to appear in J. Geometric Analysis 18(2008), no. 3Complex Variables32M05, 32C10text