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arXiv · 2512.08190

On the knot types of periodic Reeb orbits of dynamically convex contact forms

Umberto L. Hryniewicz·Pedro A. S. Salomão·Richard Siefring
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Abstract

We exhibit transverse knot types on the standard contact $3$-sphere that cannot be realized as periodic Reeb orbits of a dynamically convex contact form. In particular, such transverse knot types do not arise as closed characteristics of strictly convex energy levels on a four dimensional symplectic vector space.

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Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring. 2025-12-09. On the knot types of periodic Reeb orbits of dynamically convex contact forms. https://arxiv.org/abs/2512.08190

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