Sharp systolic inequalities for invariant tight contact forms on principal S1-bundles over S2
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909221961859072 |
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| author | Vialaret, Simon |
| author_facet | Vialaret, Simon |
| contents | The systole of a contact form $α$ is defined as the shortest period of closed Reeb orbits of $α$. Given a non-trivial $\mathbb S^1$-principal bundle over $\mathbb S^2$ with total space $M$, we prove a sharp systolic inequality for the class of tight contact form on $M$ invariant under the $\mathbb S^1$-action. This inequality exhibits a behavior which depends on the Euler class of the bundle in a subtle way. As applications, we prove a sharp systolic inequality for rotationally symmetric Finsler metrics on $\mathbb S^2$, a systolic inequality for the shortest contractible closed Reeb orbit, and a particular case of a conjecture by Viterbo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp systolic inequalities for invariant tight contact forms on principal S1-bundles over S2 Vialaret, Simon Symplectic Geometry Differential Geometry Dynamical Systems The systole of a contact form $α$ is defined as the shortest period of closed Reeb orbits of $α$. Given a non-trivial $\mathbb S^1$-principal bundle over $\mathbb S^2$ with total space $M$, we prove a sharp systolic inequality for the class of tight contact form on $M$ invariant under the $\mathbb S^1$-action. This inequality exhibits a behavior which depends on the Euler class of the bundle in a subtle way. As applications, we prove a sharp systolic inequality for rotationally symmetric Finsler metrics on $\mathbb S^2$, a systolic inequality for the shortest contractible closed Reeb orbit, and a particular case of a conjecture by Viterbo. |
| title | Sharp systolic inequalities for invariant tight contact forms on principal S1-bundles over S2 |
| topic | Symplectic Geometry Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2403.02228 |