Non R-covered Anosov flows in hyperbolic 3-manifolds are quasigeodesic
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910034313609216 |
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| author | Fenley, Sergio R |
| author_facet | Fenley, Sergio R |
| contents | The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it supports a quasigeodesic flow. We prove the continuous extension property for the stable and unstable foliations of any Anosov flow in a closed hyperbolic three manifold, and the existence of group invariant Peano curves associated with any such flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09238 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non R-covered Anosov flows in hyperbolic 3-manifolds are quasigeodesic Fenley, Sergio R Dynamical Systems Geometric Topology Primary: 57R30, 37E10, 37D20, Secondary: 53C12, 37C27, 37D05, 37C86 The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it supports a quasigeodesic flow. We prove the continuous extension property for the stable and unstable foliations of any Anosov flow in a closed hyperbolic three manifold, and the existence of group invariant Peano curves associated with any such flow. |
| title | Non R-covered Anosov flows in hyperbolic 3-manifolds are quasigeodesic |
| topic | Dynamical Systems Geometric Topology Primary: 57R30, 37E10, 37D20, Secondary: 53C12, 37C27, 37D05, 37C86 |
| url | https://arxiv.org/abs/2210.09238 |