2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59815We classify all connected $n$-dimensional complex manifolds admitting an effective action of the unitary group $U_n$ by biholomorphic transformations. One consequence of this classification is a characterization of ${\bf C}^n$ by its automorphism group.Also available from http://wwwmaths.anu.edu.au/research.reports/00mrr.htmlComplex Variables32Q57, 32M17text