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On the complete integrability of the geodesic flow of manifoldsall of whose geodesics are closed

Published online by Cambridge University Press:  01 December 1997

CARLOS E. DURÁN
CARLOS E. DURÁN
Affiliation:
IMPA, Estrada Dona Castorina 110, Jardim Botânico 22460-320, Rio de Janeiro RJ, Brasil (e-mail: [email protected]) Current address: IVIC-Matemáticas, Aptdo 21827, Caracas 1020A, Venezuela.
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 6 , December 1997 , pp. 1359 - 1370
Copyright
1997 Cambridge University Press

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