Effective actions of the unitary group on complex manifolds

2000/08/29 by Alexander Isaev, A. V. Isaev, Isaev, A. V. +2
Mathematics · #32M17 #32Q57 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #msc:32M17 #msc:32Q57

paper · pdf · doi:10.48550/arxiv.math/0008219

Also available from http://wwwmaths.anu.edu.au/research.reports/00mrr.html

arxiv created 2000/08/29 · openalex publication_date 2000/08/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify all connected n-dimensional complex manifolds admitting an effective action of the unitary group U_n by biholomorphic transformations. One consequence of this classification is a characterization of \bf Cⁿ by its automorphism group.

Citations

• On the automorphism groups of hyperbolic manifolds

Related

• Effective actions of SU_n on complex n-dimensional manifolds
• Effective actions of the general indefinite unitary groups on holomorphically separable manifolds
• Proper actions of high-dimensional groups on complex manifolds
• Automorphisms of \mathbb C^k and associated compact complex manifolds
• Classical Symmetries of Complex Manifolds