Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid

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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).

Original languageEnglish (US)
Pages (from-to)306-321
Number of pages16
JournalCommentarii Mathematici Helvetici
Volume74
Issue number2
DOIs
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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