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

Fuente: arXiv
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Main Author: Ferreira, Brayan
Format: Preprint
Published: 2023
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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