Complete hyperbolic Stein manifolds with prescribed automorphism groups

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dc.creatorKan, Su-Jen
dc.date2004-12-21
dc.date.accessioned2026-07-07T05:15:32Z
dc.date.available2026-07-07T05:15:32Z
dc.descriptionIt is well-known that the automorphism group of a hyperbolic manifold is a Lie group.Conversely, it is interesting to see whether or not any Lie group could be prescribed asthe automorphism group of certain complex manifold. Whenthe Lie group $G$ is compact and connected, this problem has been completelysolved by Bedford-Dadok and independently by Saerens-Zame on 1987. Theyhave constructed \spc bounded domains $Ω$ such that $Aut(Ω)=G$. For Bedford-Dadok's $Ω, 0\le dim_{\Bbb C}Ω- dim_{\Bbb R}G\le 1$; for generic Saerens-Zame's$Ω,dim_{\Bbb C}Ω\gg dim_{\Bbb R}G$.J. Winkelmann has answered affirmatively to noncompact connected Liegroups in recent years. He showed there exist Stein complete hyperbolic manifolds $Ω$ such that $Aut(Ω)=G$.In his construction, it is typical that $dim_{\Bbb C}Ω\gg dim_{\Bbb R}G$.In this article, we tackle this problem from a different aspect. We provethat for any connected Lie group $G$ (compact or noncompact), there exist completehyperbolic Stein manifolds $Ω$ such that $Aut(Ω)=G$ with $dim_{\BbbC}Ω=dim_{\Bbb R}G.$ Working on a natural complexification of the real-analyticmanifold $G$, our construction of $Ω$ is geometrically concrete andelementary in nature.
dc.description14 pages, submitted
dc.identifierhttps://arxiv.org/abs/math/0412420
dc.identifierhttp://arxiv.org/abs/math/0412420
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73659
dc.subjectComplex Variables
dc.subject32C09, 32Q28
dc.titleComplete hyperbolic Stein manifolds with prescribed automorphism groups
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