Abstract.
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).
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Received: March 10, 1998.
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Tabachnikov, S. Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid. Comment. Math. Helv. 74, 306–321 (1999). https://doi.org/10.1007/s000140050091
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DOI: https://doi.org/10.1007/s000140050091