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Integrable geodesic flows on homogeneous spaces

Published online by Cambridge University Press:  19 September 2008

A. Thimm
A. Thimm
Affiliation:
Mathematisches Institut der Universität Bonn, Wegelerstrasse 10, D5300 Bonn 1, West Germany
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Abstract

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A method is exposed which allows the construction of families of first integrals in involution for Hamiltonian systems which are invariant under the Hamiltonian action of a Lie group G. This is applied to invariant Hamiltonian systems on the tangent bundles of certain homogeneous spaces M = G/K. It is proved, for example, that every such invariant Hamiltonian system is completely integrable if M is a real or complex Grassmannian manifold or SU(n + 1)/SO(n + 1) or a distance sphere in ℂPn+1. In particular, the geodesic flows of these homogeneous spaces are integrable.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 495 - 517
Copyright
Copyright © Cambridge University Press 1981

References

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