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arXiv · 2503.08077

Horizontality of partially hyperbolic foliations

Andy Hammerlindl·Rafael Potrie
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Abstract

We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also show for these systems that the center-stable and center-unstable foliations can be isotoped so that their leaves are transverse to the circle fibering. As a consequence, every partially hyperbolic system defined on the unit tangent bundle of a higher-genus surface is a collapsed Anosov flow.

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Andy Hammerlindl, Rafael Potrie. 2025-03-11. Horizontality of partially hyperbolic foliations. https://arxiv.org/abs/2503.08077

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