Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid
نویسنده
چکیده
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). Mathematics Subject Classification (1991). 53.
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