The geometry of Randers cylinders of revolution with non-constant navigation data along meridians
Volume 131 / 2023
Annales Polonici Mathematici 131 (2023), 97-125
MSC: Primary 53C60; Secondary 53C22, 53C20.
DOI: 10.4064/ap221017-13-8
Published online: 14 November 2023
Abstract
We study the structure of cut loci of a Finsler metric of Randers type defined on a cylindrical surface of revolution. Our Randers metrics are obtained by perturbing the Riemannian metric with a closed one-form, which is equivalent to the solution of Zermelo’s navigation problem for a wind blowing along meridians. We describe the Riemannian part by a solution of a Riccati type differential equation approach that allows a better control of cut loci and construction of examples. We establish the conditions for the Finsler metric to have the same cut locus structure as in the Riemannian case, giving several examples.
