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On the complete integrability of the geodesic flow of manifolds all of whose geodesics are closed

  • CARLOS E. DURÁN (a1) (a2)

Abstract

We show that the geodesic flow of a metric all of whose geodesics are closed is completely integrable, with tame integrals of motion. Applications to classical examples are given; in particular, it is shown that the geodesic flow of any quotient $M/\Gamma$ of a compact, rank one symmetric space $M$ by a finite group acting freely by isometries is completely integrable by tame integrals.

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On the complete integrability of the geodesic flow of manifolds all of whose geodesics are closed

  • CARLOS E. DURÁN (a1) (a2)

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