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Effective Actions of the Unitary Group on Complex Manifolds

Published online by Cambridge University Press:  20 November 2018

A. V. Isaev  and
N. G. Kruzhilin
A. V. Isaev
Affiliation:
Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, Australia, e-mail: Alexander.Isaev@anu.edu.au
N. G. Kruzhilin
Affiliation:
Department of Complex Analysis, Steklov Mathematical Institute, 42 Vavilova St. Moscow 117966, Russia, e-mail: kruzhil@ns.ras.ru
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Abstract

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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 ${{\mathbb{C}}^{n}}$ by its automorphism group.

Keywords

32Q5732M17complex manifoldsgroup actions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 6 , 01 December 2002 , pp. 1254 - 1279
Copyright
Copyright © Canadian Mathematical Society 2002

References

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