Commentarii Mathematici Helvetici
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Published online: 1999-06-30
Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoidS. Tabachnikov (1) University of Arkansas, Fayetteville, USA
We give a new proof of the complete integrability of the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose non-parameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperbolic metric inside the ellipsoid (Klein's model).
Keywords: Riemannian and Finsler metrics, symplectic and contact structures, geodesic flow, exact transverse line fields
Tabachnikov S.: Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid. Comment. Math. Helv. 74 (1999), 306-321. doi: 10.1007/s000140050091