On real trigonal Riemann surfaces - Costa, Antonio F.; Izquierdo, Milagros (MATHEMATICA SCANDINAVICA, 2006)
A closed Riemann surface X which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface X is called real trigonal if there is an anticonformal involution (symmetry) σ of X commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry σ is the number of connected components of the fixed point set Fix(σ) and the orientability of the Klein surface X/σ. We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.