Authors: Jovanović, Božidar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the integrability of geodesic flows of submersion metrics
Journal: Letters in Mathematical Physics
Volume: 61
Issue: 1
First page: 29
Last page: 39
Issue Date: 1-Jan-2002
Rank: M22
ISSN: 0377-9017
DOI: 10.1023/A:1020234130071
Suppose we are given a compact Riemannian manifold (Q, g) with a completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by isometrics. 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.
Keywords: Integrable geodesic flows | Noncommutative integrability | Symplectic reduction
Publisher: Springer Link
Project: Serbian Ministry of Science and Technology, Project 1643 – Geometry and Topology of Manifolds and Integrable Dynamical Systems

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