Effective actions of the unitary group on complex manifolds

Alexander V. Isaev; N. G. Kruzhilin

doi:10.4153/CJM-2002-048-2

Effective actions of the unitary group on complex manifolds

Alexander V. Isaev^*, N. G. Kruzhilin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

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 ℂⁿ by its automorphism group.

Original language	English
Pages (from-to)	1254-1279
Number of pages	26
Journal	Canadian Journal of Mathematics
Volume	54
Issue number	6
DOIs	https://doi.org/10.4153/CJM-2002-048-2
Publication status	Published - 2002

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title = "Effective actions of the unitary group on complex manifolds",

abstract = "We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of ℂn by its automorphism group.",

keywords = "Complex manifolds, Group actions",

author = "Isaev, \{Alexander V.\} and Kruzhilin, \{N. G.\}",

year = "2002",

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language = "English",

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pages = "1254--1279",

journal = "Canadian Journal of Mathematics",

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AU - Isaev, Alexander V.

AU - Kruzhilin, N. G.

PY - 2002

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N2 - We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of ℂn by its automorphism group.

AB - We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of ℂn by its automorphism group.

KW - Complex manifolds

KW - Group actions

UR - https://www.scopus.com/pages/publications/0036978035

U2 - 10.4153/CJM-2002-048-2

DO - 10.4153/CJM-2002-048-2

M3 - Article

SN - 0008-414X

VL - 54

SP - 1254

EP - 1279

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 6

ER -

Effective actions of the unitary group on complex manifolds

Abstract

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