Integrable geodesic flows with simultaneously diagonalisable quadratic integrals
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917383143161856 |
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| author | Agafonov, Sergey I. Matveev, Vladimir S. |
| author_facet | Agafonov, Sergey I. Matveev, Vladimir S. |
| contents | We show that if $n$ functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an $n$-dimensional manifold are simultaneously diagonalisable at the tangent space to every point, then they come from the Stäckel construction, so the metric admits orthogonal separation of variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable geodesic flows with simultaneously diagonalisable quadratic integrals Agafonov, Sergey I. Matveev, Vladimir S. Differential Geometry Mathematical Physics Dynamical Systems Exactly Solvable and Integrable Systems 37J35, 70H06 We show that if $n$ functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an $n$-dimensional manifold are simultaneously diagonalisable at the tangent space to every point, then they come from the Stäckel construction, so the metric admits orthogonal separation of variables. |
| title | Integrable geodesic flows with simultaneously diagonalisable quadratic integrals |
| topic | Differential Geometry Mathematical Physics Dynamical Systems Exactly Solvable and Integrable Systems 37J35, 70H06 |
| url | https://arxiv.org/abs/2403.14319 |