Abstract
In the study of geodesics on surfaces, the subjects and methods are different for spheres, tori, other closed surfaces and non-compact surfaces. We make the method used to study geodesics on 2-tori applicable to surfaces with genus 2 or higher. Let be a torus with boundary embedded in an orientable geodesically complete Finsler surface . We define a distance on in such a way that is the minimum length of curves in from to homotopic to curves in with same endpoints . Those geodesics are minimal with respect to but not in . We use this distance to study geodesics in homotopic to curves in .
Funding Statement
Research was partially supported by the JSPS KAKENHI Grant Number JP18K03314.
Citation
Nobuhiro Innami. Yoe Itokawa. Tetsuya Nagano. Katsuhiro Shiohama. "Axial straight lines in the covering surface of a Finsler surface." Nihonkai Math. J. 32 (1) 15 - 24, 2021.
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