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Journal Articles Documenta Mathematica Year : 2009

On proper $\mathbb{R}$-actions on hyperbolic Stein surfaces

Abstract

In this paper we investigate proper $\mathbb{R}$--actions on hyperbolic Stein surfaces and prove in particular the following result: Let $D\subset\mathbb{C}^2$ be a simply-connected bounded domain of holomorphy which admits a proper $\mathbb{R}$--action by holomorphic transformations. The quotient $D/\mathbb{Z}$ with respect to the induced proper $\mathbb{Z}$--action is a Stein manifold. A normal form for the domain $D$ is deduced.
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Dates and versions

hal-00397054 , version 1 (19-06-2009)

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  • HAL Id : hal-00397054 , version 1

Cite

Christian Miebach, Karl Oeljeklaus. On proper $\mathbb{R}$-actions on hyperbolic Stein surfaces. Documenta Mathematica, 2009, 14, pp.673--689. ⟨hal-00397054⟩
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