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arXiv · 2602.00439

Finiteness of Totally Magnetic Hypersurfaces

James Marshall Reber·Ivo Terek
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Abstract

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.

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James Marshall Reber, Ivo Terek. 2026-01-31. Finiteness of Totally Magnetic Hypersurfaces. https://doi.org/10.3842/sigma.2026.043

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