Elliptic Reeb orbit on some real projective three-spaces via ECH
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915334014894080 |
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| author | Ferreira, Brayan |
| author_facet | Ferreira, Brayan |
| contents | We prove the existence of an elliptic Reeb orbit for some contact forms on the real projective three space $\mathbb{R} P^3$. The main ingredient of the proof is the existence of a distinguished pseudoholomorphic curve in the symplectization given by the $U$ map on ECH. Also, we check that the first value on the ECH spectrum coincides with the smallest action of null-homologous orbit sets for $1/4$-pinched Riemannian metrics and compute the ECH spectrum for the irrational Katok metric example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06257 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Elliptic Reeb orbit on some real projective three-spaces via ECH Ferreira, Brayan Symplectic Geometry Differential Geometry Dynamical Systems 53D10, 53D25, 53D42 We prove the existence of an elliptic Reeb orbit for some contact forms on the real projective three space $\mathbb{R} P^3$. The main ingredient of the proof is the existence of a distinguished pseudoholomorphic curve in the symplectization given by the $U$ map on ECH. Also, we check that the first value on the ECH spectrum coincides with the smallest action of null-homologous orbit sets for $1/4$-pinched Riemannian metrics and compute the ECH spectrum for the irrational Katok metric example. |
| title | Elliptic Reeb orbit on some real projective three-spaces via ECH |
| topic | Symplectic Geometry Differential Geometry Dynamical Systems 53D10, 53D25, 53D42 |
| url | https://arxiv.org/abs/2305.06257 |