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# Effective Actions of the Unitary Group on Complex Manifolds

Published:2002-12-01
Printed: Dec 2002
• A. V. Isaev
• N. G. Kruzhilin
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## Abstract

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 actions
 MSC Classifications: 32Q57 - Classification theorems 32M17 - Automorphism groups of ${\bf C}^n$ and affine manifolds

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