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

Serge Tabachnikov | Zendy

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

Author(s) -

Serge Tabachnikov

Publication year - 1999

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050091

Subject(s) - ellipsoid , geodesic , mathematics , metric (unit) , mathematical analysis , parameterized complexity , pure mathematics , flow (mathematics) , hyperbolic space , metric space , geometry , combinatorics , physics , operations management , astronomy , economics

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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