Transverse minimal foliations on unit tangent bundles and applications

Autor:	Fenley, Sergio R., Potrie, Rafael
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology Mathematics - Differential Geometry Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 64 pages, 20 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.14525 Zobrazit plný text záznamu View this record from Arxiv