Abstract:
On the triaxial ellipsoid we consider curvature lines and geodesics and null-geodesics. We
discuss when the curvature lines define a foliation with non-compact leaves.
We also show that compact geodesics
correspond to $2$-fold coverings of an elliptic curve by a curve of genus $2$ and extend this to
null-geodesics. These problems lead to
determine the dimension of elliptic and abelian period spaces which is related to Schneider's
$3$rd and $4$th problem in his monograph on transcendental numbers.
