A classification of taut, Stein surfaces with a proper $\mathbb{R}$-action

Abstract

We present a classification of 2-dimensional, taut, Stein manifolds with a proper $\mathbb{R}$-action. For such manifolds the globalization with respect to the induced local $\C$-action turns out to be Stein. As an application we determine all 2-dimensional taut, non-complete, Hartogs domains over a Riemann surface.

v3: proof of Prop. 4.1 changed and minor changes