A classification of taut, Stein surfaces with a proper $R$-action

We present a classification of 2-dimensional, taut, Stein manifolds with a proper $R$-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.