Geodesics on an ellipsoid in Minkowski space

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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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Differential Geometry, Dynamical Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/128231

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.0188
 http://arxiv.org/abs/0705.0188

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arXiv