On the integrability of geodesic flows of submersion metrics
Abstract
Suppose we are given a compact Riemannian manifold (Q,g)with completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by isometries. The natural question arises: will the geodesic flow on Q/G equipped with the submersion metric be integrable? Under one natural assumption, we prove that the answer is affirmative. New examples of manifolds with completely integrable geodesic flows are obtained.
 Publication:

arXiv eprints
 Pub Date:
 April 2002
 arXiv:
 arXiv:mathph/0204048
 Bibcode:
 2002math.ph...4048J
 Keywords:

 Mathematical Physics;
 Dynamical Systems;
 70H06;
 37J35;
 53D25
 EPrint:
 10 pages, minor changes