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 | Abstract: | 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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