Algebraic Closed Geodesics on a Triaxial Ellipsoid *
نویسنده
چکیده
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 R. Such geodesics are either connected components of spatial elliptic curves or of rational curves. Our approach is based on elements of the Weierstrass–Poncaré reduction theory for hyperelliptic tangential covers of elliptic curves, the addition law for elliptic functions, and the Moser– Trubowitz isomorphism between geodesics on a quadric and stationary solutions of the KdV equation. 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.
منابع مشابه
2 9 Ju n 20 05 Algebraic Closed Geodesics on a Triaxial Ellipsoid ∗
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 R. 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...
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