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Keywords = Rieman surface

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30 pages, 2236 KB  
Article
An Affine Model of a Riemann Surface Associated to a Schwarz–Christoffel Mapping
by Richard Cushman
Axioms 2021, 10(2), 49; https://doi.org/10.3390/axioms10020049 - 1 Apr 2021
Viewed by 2245
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Applications of Differential Geometry II)
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