Proper actions of Lie groups of dimension \(n^{2} + 1\) on \(n\)-dimensional complex manifolds
type: Item
instance of: scholarly article
title: Proper actions of Lie groups of dimension \(n^{2} + 1\) on \(n\)-dimensional complex manifolds
zbMATH Open document ID: 1175.32009
author: N. G. Kruzhilin
author: A. V. Isaev
published in: Israel Journal of Mathematics
publication date: 2009-10-02T00:00:00Z
review text: The authors continue a study of actions of high-dimensional Lie groups on complex manifolds. They give explicit description of all pairs \((M,G)\), where \(M\) is a connected complex manifold of dimension \(n\geq 2\) and \(G\) is a connected Lie group of dimension \(n^2+1\) acting effectively and properly on \(M\) by holomorphic transformations. The result complements a classification obtained earlier by the first author for \(n^2+2\leq\dim\;G<n^2+2n\) and a classical result due to W. Kaup for the maximal group dimension \(n^2+2n\).
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 5610605
zbMATH Keywords: proper actions
zbMATH Keywords: complex manifolds
zbMATH Keywords: complex Lie group
zbMATH Keywords: holomorphic transformation
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
full work available at URL: s11856-009-0071-4
OpenAlex ID: W2964248515
cites work: Q4833694
cites work: ON PERFECT ACTIONS OF LIE GROUPS
cites work: Proper actions on cohomology manifolds
cites work: Compact groups of differentiable transformations
cites work: Groups of differentiable and real or complex analytic transformations
cites work: Locally compact groups of differentiable transformations
cites work: Variations of Hartogs' theorem
cites work: Q5797635
cites work: Q4172188
cites work: Q5734920
cites work: A Classification of Homogeneous Surfaces
cites work: Hyperbolic manifolds of dimension \(n\) with automorphism group of dimension \(n^2-1\)
cites work: Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism group
cites work: Hyperbolic \(n\)-dimensional manifolds with automorphism group of dimension \(n^2\)
cites work: Lectures on the automorphism groups of Kobayashi-hyperbolic manifolds
cites work: Proper actions of high-dimensional groups on complex manifolds
cites work: Q3515846
cites work: On the automorphism groups of hyperbolic manifolds
cites work: Effective Actions of the Unitary Group on Complex Manifolds
cites work: Homogeneous Riemannian spaces of four dimensions
cites work: Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen
cites work: Q5608188
cites work: Q5658761
cites work: Q5664533
cites work: Q3235032
cites work: Sur La Forme Hermitienne Canonique Des Espaces Homogenes Complexes
cites work: On \(n\)-dimensional homogeneous spaces of Lie groups of dimension greater than \({1\over 2}n(n-1)\)
cites work: Homogeneous complex surfaces
cites work: Q4284481
cites work: Q3998356
cites work: On the existence of slices for actions of non-compact Lie groups
cites work: Classifying 3 and 4 dimensional homogeneous Riemannian manifolds by Cartan triples
cites work: Q3941676
cites work: On Finsler Spaces with Completely Integrable Equations of Killing
cites work: The classification of three-dimensional homogeneous complex manifold
cites work: On n-Dimensional Riemannian Spaces Admitting a Group of Motions of Order n(n-1)/2 + 1
cites work: Q3241635
DOI: 10.1007/S11856-009-0071-4
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description: scientific article; zbMATH DE number 5610605