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 ${\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic curves or rational curves.   Our approach is based on elements of the Weierstrass--Poncar\'e 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. 
Yuri Fedorov