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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.01566 |
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| _version_ | 1866911426623307776 |
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| author | Mironov, Andrey E. Yin, Siyao |
| author_facet | Mironov, Andrey E. Yin, Siyao |
| contents | In this paper we study the behavior of geodesics on cones over arbitrary $C^3$-smooth closed Riemannian manifolds. We show that the geodesic flow on such cones admits first integrals whose values uniquely determine almost all geodesics except for radial geodesics; thus, the geodesic flow is superintegrable. Moreover, we prove that the geodesic flow restricted to the open dense subset of the cotangent bundle corresponding to all non-radial trajectories is Liouville--Arnold integrable. This investigation is inspired by our recent results on Birkhoff billiards inside cones over convex manifolds where similar results hold true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrable Geodesic Flows on Cones over Riemannian Manifolds Mironov, Andrey E. Yin, Siyao Differential Geometry In this paper we study the behavior of geodesics on cones over arbitrary $C^3$-smooth closed Riemannian manifolds. We show that the geodesic flow on such cones admits first integrals whose values uniquely determine almost all geodesics except for radial geodesics; thus, the geodesic flow is superintegrable. Moreover, we prove that the geodesic flow restricted to the open dense subset of the cotangent bundle corresponding to all non-radial trajectories is Liouville--Arnold integrable. This investigation is inspired by our recent results on Birkhoff billiards inside cones over convex manifolds where similar results hold true. |
| title | Integrable Geodesic Flows on Cones over Riemannian Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.01566 |