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Algebraic Closed Geodesics on a Triaxial Ellipsoid

Yuri Fedorov
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Abstract

We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic curves or rational curves. Our approach is based on elements of the Weierstrass--Poncaré reduction theory for hyperelliptic tangential covers of elliptic curves and the addition law for elliptic functions. For the case of 3-fold and 4-fold coverings, explicit formulas for the cutting algebraic surfaces are provided and some properties of the corresponding geodesics are discussed.

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Yuri Fedorov. 2005-10-10. Algebraic Closed Geodesics on a Triaxial Ellipsoid. https://doi.org/10.1070/rd2005v010n04abeh000326

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