Search: MSC category 32M17 ( Automorphism groups of ${\bf C}^n$ and affine manifolds )
 Effective Actions of the Unitary Group on Complex Manifolds We classify all connected $n$-dimensional complex manifolds admitting effective actions of the unitary group $U_n$ by biholomorphic transformations. One consequence of this classification is a characterization of $\CC^n$ by its automorphism group. Keywords:complex manifolds, group actionsCategories:32Q57, 32M17