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Effective Actions of the Unitary Group on Complex Manifolds

Open Access article
 Printed: Dec 2002
  • A. V. Isaev
  • N. G. Kruzhilin
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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 complex manifolds, group actions
MSC Classifications: 32Q57, 32M17 show english descriptions Classification theorems
Automorphism groups of ${\bf C}^n$ and affine manifolds
32Q57 - Classification theorems
32M17 - Automorphism groups of ${\bf C}^n$ and affine manifolds

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