Closed Riemann surfaces with dihedral groups of conformal automorphisms

Abstract

In these notes we show that if H is a group of conformal automorphisms, isomorphic to a dihedral group, acting free fixed points on a closed Riemann surface S, then there is a Schottky uniformization of S for which H lifts. We also give an explicit example of a dihedral group for which the above lifting property fails, showing in this way that condition (A) of [4] is not sufficient in general.