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

Abstract

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

15 pages

References in corpus (1)

• Quotients of bounded homogeneous domains by cyclic groups

Cited by in corpus (2)

• A classification of taut, Stein surfaces with a proper $\mathbb{R}$-action
• Quotients of the crown domain by a proper action of a cyclic group