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The real vector space ๐‘…3 equipped with the elliptical inner product ๐ต : ๐‘…3 ร— ๐‘…3 โ†’ ๐‘…; ๐ต(๐‘ข, ๐‘ฃ) = ๐‘Ž1๐‘ฅ1๐‘ฆ1 + ๐‘Ž2๐‘ฅ2๐‘ฆ2 + ๐‘Ž3๐‘ฅ3๐‘ฆ3

Preliminaries In this section, we present brief information of the structures on the elliptical 2-sphere ๐‘†๐ธ 2 to describe the basic background

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math.GM 1

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Elliptical trajectories of a point on the elliptical 2-sphere

math.GM ยท 2019-08-07 ยท reject ยท novelty 3.0

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 math.GM ยท 2019-08-07 ยท reject ยท none ยท ref 2

    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.