Transverse minimal foliations on unit tangent bundles and applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909013707325440 |
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| author | Fenley, Sergio R. Potrie, Rafael |
| author_facet | Fenley, Sergio R. Potrie, Rafael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14525 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transverse minimal foliations on unit tangent bundles and applications Fenley, Sergio R. Potrie, Rafael Geometric Topology Differential Geometry Dynamical Systems 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. |
| title | Transverse minimal foliations on unit tangent bundles and applications |
| topic | Geometric Topology Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2303.14525 |