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arXiv · 2305.06257

Elliptic Reeb orbit on some real projective three-spaces via ECH

Brayan Ferreira
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Abstract

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.

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Brayan Ferreira. 2023-05-10. Elliptic Reeb orbit on some real projective three-spaces via ECH. https://doi.org/10.4171/rmi%2F1480

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