The paper derives Darboux-frame equations, Killing equations, and parametric formulas for magnetic curves and helices on an ellipsoid equipped with an anisotropic metric, but the results are reparametrizations of standard spherical curve results.
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Elliptical trajectories of a point on the elliptical 2-sphere
The paper derives Darboux-frame equations, Killing equations, and parametric formulas for magnetic curves and helices on an ellipsoid equipped with an anisotropic metric, but the results are reparametrizations of standard spherical curve results.