Finiteness of Totally Magnetic Hypersurfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913082082590720 |
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| author | Reber, James Marshall Terek, Ivo |
| author_facet | Reber, James Marshall Terek, Ivo |
| contents | By introducing a dynamical version of the second fundamental form, we generalize a recent result of Filip-Fisher-Lowe to the setting of magnetic systems. Namely, we show that a real-analytic negatively $s$-curved magnetic system on a closed real-analytic manifold has only finitely many closed totally $s$-magnetic hypersurfaces, unless the magnetic 2-form is trivial and the underlying metric is hyperbolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finiteness of Totally Magnetic Hypersurfaces Reber, James Marshall Terek, Ivo Differential Geometry Dynamical Systems 37D20, 37D40, 53C15, 53C20 By introducing a dynamical version of the second fundamental form, we generalize a recent result of Filip-Fisher-Lowe to the setting of magnetic systems. Namely, we show that a real-analytic negatively $s$-curved magnetic system on a closed real-analytic manifold has only finitely many closed totally $s$-magnetic hypersurfaces, unless the magnetic 2-form is trivial and the underlying metric is hyperbolic. |
| title | Finiteness of Totally Magnetic Hypersurfaces |
| topic | Differential Geometry Dynamical Systems 37D20, 37D40, 53C15, 53C20 |
| url | https://arxiv.org/abs/2602.00439 |