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

TL;DR

This paper classifies 2D taut Stein surfaces with proper real actions, showing their globalizations are Stein and identifying all such non-complete Hartogs domains over Riemann surfaces.

Contribution

It provides a complete classification of 2D taut Stein surfaces with proper -action, including their globalizations and specific examples over Riemann surfaces.

Findings

Globalizations of these surfaces are Stein.

All 2D taut, non-complete Hartogs domains over Riemann surfaces are classified.

Abstract

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.