Elliptic Reeb orbit on some real projective three-spaces via ECH
Brayan Ferreira
Universidade Federal do Espírito Santo, Vitória, Brazil
![Elliptic Reeb orbit on some real projective three-spaces via ECH cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-rmi.png&w=3840&q=90)
Abstract
We prove the existence of an elliptic Reeb orbit for some contact forms on the real projective three space . The main ingredient of the proof is the existence of a distinguished pseudoholomorphic curve in the symplectization given by the 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 -pinched Riemannian metrics. This action coincides with twice the length of a shortest closed geodesic. In addition, we compute the ECH spectrum for the irrational Katok metric example.
Cite this article
Brayan Ferreira, Elliptic Reeb orbit on some real projective three-spaces via ECH. Rev. Mat. Iberoam. (2024), published online first
DOI 10.4171/RMI/1480