Magnetic Killing tensors and first integrals of the magnetic flow
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912916067844096 |
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| author | Moroianu, Andrei Ovando, Gabriela |
| author_facet | Moroianu, Andrei Ovando, Gabriela |
| contents | In this work we introduce a new family of symmetric tensors generalizing Killing tensors, that we call magnetic Killing symmetric tensors. We make use of them to construct first integrals for the magnetic flow associated to a given magnetic field. We apply the results to prove integrability of some invariant magnetic flows (either exact or non-exact) on some 2-step nilmanifolds: the Kodaira-Thurston manifold and Heisenberg nilmanifolds of higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18373 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magnetic Killing tensors and first integrals of the magnetic flow Moroianu, Andrei Ovando, Gabriela Differential Geometry Dynamical Systems In this work we introduce a new family of symmetric tensors generalizing Killing tensors, that we call magnetic Killing symmetric tensors. We make use of them to construct first integrals for the magnetic flow associated to a given magnetic field. We apply the results to prove integrability of some invariant magnetic flows (either exact or non-exact) on some 2-step nilmanifolds: the Kodaira-Thurston manifold and Heisenberg nilmanifolds of higher dimensions. |
| title | Magnetic Killing tensors and first integrals of the magnetic flow |
| topic | Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2602.18373 |