Transverse minimal foliations on unit tangent bundles and applications

Sergio R. Fenley; Rafael Potrie

doi:10.2140/pjm.2026.343.39

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arXiv · 2303.14525

Transverse minimal foliations on unit tangent bundles and applications

Sergio R. Fenley·Rafael Potrie

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Abstract

We show that if $\mathcal{F}_1$ and $\mathcal{F}_2$ are two transverse minimal foliations on $M = T^1S$ then either they intersect in an Anosov foliation or there exists a Reeb-surface in the intersection foliation. The existence of a Reeb surface is incompatible with partially hyperbolic foliations so we deduce from this that certain partially hyperbolic diffeomorphisms in unit tangent bundles are collapsed Anosov flows. We also conclude that every volume preserving partially hyperbolic diffeomorphism of a unit tangent bundle is ergodic.

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BibTeX RIS

Sergio R. Fenley, Rafael Potrie. 2023-03-25. Transverse minimal foliations on unit tangent bundles and applications. https://doi.org/10.2140/pjm.2026.343.39

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