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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.19979 |
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| _version_ | 1866908420819386368 |
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| author | Dehornoy, Pierre Rechtman, Ana |
| author_facet | Dehornoy, Pierre Rechtman, Ana |
| contents | A flow on a 3-manifold is left-handed if any two ergodic invariant measures have negative linking number. We prove that on a 2-sphere of revolution whose curvature is $1/4$-pinched the geodesic flow is left-handed. Conversely, for every $δ\le 1/4$, we construct a 2-sphere whose curvature is $δ$-pinched and whose geodesic flow is not left-handed. This gives credit to a conjecture of Florio and Hryniewicz that $1/4$ is the optimal pinching constant for left-handedness among arbitrary positively curved 2-spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left-handed geodesic flow of spheres of revolution Dehornoy, Pierre Rechtman, Ana Dynamical Systems 37D40 (Primary), 53D25 (secondary) A flow on a 3-manifold is left-handed if any two ergodic invariant measures have negative linking number. We prove that on a 2-sphere of revolution whose curvature is $1/4$-pinched the geodesic flow is left-handed. Conversely, for every $δ\le 1/4$, we construct a 2-sphere whose curvature is $δ$-pinched and whose geodesic flow is not left-handed. This gives credit to a conjecture of Florio and Hryniewicz that $1/4$ is the optimal pinching constant for left-handedness among arbitrary positively curved 2-spheres. |
| title | Left-handed geodesic flow of spheres of revolution |
| topic | Dynamical Systems 37D40 (Primary), 53D25 (secondary) |
| url | https://arxiv.org/abs/2506.19979 |