An Affine Model of a Riemann Surface Associated to a Schwarz–Christoffel Mapping

Abstract

In this paper, we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz–Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on this Riemann surface and billiard motions in a regular stellated n-gon in the complex plane.

Keywords

• Schwarz–Christofell
• Rieman surface
• discrete subgroup