Geodesics on an ellipsoid in Minkowski space
Differential Geometry
2007-05-23 v1 Dynamical Systems
Abstract
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic close up after several oscillations in the "pseudo-Riemannian belt", so do all other null geodesics on this ellipsoid.
Cite
@article{arxiv.0705.0188,
title = {Geodesics on an ellipsoid in Minkowski space},
author = {D. Genin and B. Khesin and S. Tabachnikov},
journal= {arXiv preprint arXiv:0705.0188},
year = {2007}
}