Transverse minimal foliations on unit tangent bundles and applications

2023/03/25 by Fenley, Sergio R., Potrie, Rafael · 1 citation
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2303.14525

Abstract

We show that if F₁ and F₂ are two transverse minimal foliations on M = T¹S 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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• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

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