Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T06:32:16.740Z Has data issue: false hasContentIssue false
  • English
  • Français

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: cduran@impa.br) Current address: IVIC-Matemáticas, Aptdo 21827, Caracas 1020A, Venezuela.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)