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arXiv · 0705.0188

Geodesics on an ellipsoid in Minkowski space

D. Genin·B. Khesin·S. Tabachnikov
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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.

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D. Genin, B. Khesin, S. Tabachnikov. 2007-05-01. Geodesics on an ellipsoid in Minkowski space. https://arxiv.org/abs/0705.0188

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