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Pré-Publication, Document De Travail Année : 2022

Quantitative conditions for right-handedness

Résumé

We give a numerical condition for right-handedness of a dynamically convex Reeb flow on S^3. Our condition is stated in terms of an asymptotic ratio between the amount of rotation of the linearised flow and the linking number of trajectories with a periodic orbit that spans a disk-like global surface of section. As an application, we find an explicit constant δ * < 0.7225 such that if a Riemannian metric on the 2-sphere is δ-pinched with δ > δ * , then its geodesic flow lifts to a right-handed flow on S^3. In particular, all finite collections of periodic orbits of such a geodesic flow bind open books whose pages are global surfaces of section.
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Dates et versions

hal-03852326 , version 1 (14-11-2022)

Identifiants

  • HAL Id : hal-03852326 , version 1

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Anna Florio, Umberto L. Hryniewicz. Quantitative conditions for right-handedness. 2022. ⟨hal-03852326⟩
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