The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed

DOI10.4171/CMH/493zbMath1455.53092arXiv1901.10617OpenAlexW2936766544MaRDI QIDQ2214028

Marco Mazzucchelli, Daniel Cristofaro-Gardiner

Publication date: 4 December 2020

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.10617

zbMATH Keywords

Seifert fibrationReeb flowembedded contact homologyBesse contact formZoll contact form

Mathematics Subject Classification ID

Contact manifolds (general theory) (53D10) Symplectic field theory; contact homology (53D42)

Related Items (6)

A Boothby-Wang theorem for Besse contact manifolds ⋮ Higher systolic inequalities for 3-dimensional contact manifolds ⋮ On the spectral characterization of Besse and Zoll Reeb flows ⋮ On the local systolic optimality of Zoll contact forms ⋮ Pseudorotations of the -disc and Reeb flows on the -sphere ⋮ On the structure of Besse convex contact spheres

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A systolic inequality for geodesic flows on the two-sphere
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Rigidity for surfaces of non-positive curvature
• Geodesics closed on the projective plane
• On metrics on \(S^ 2\) all of whose geodesics are closed
• Geodesic foliations by circles
• A foliation of geodesics is characterized by having no tangent homologies
• The dynamics on three-dimensional strictly convex energy surfaces
• The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on \(S^1\times B^3\)
• Seifert fibrations of lens spaces
• Sharp systolic inequalities for Reeb flows on the three-sphere
• Transverse contact structures on Seifert 3-manifolds
• Transformation groups in differential geometry.
• The marked length spectrum of Anosov manifolds
• A Hamiltonian version of a result of Gromoll and Grove
• The asymptotics of ECH capacities
• Zur Topologie gefaserter dreidimensionaler Mannigfaltigkeiten
• On manifolds all of whose geodesics are closed
• Lecture Notes on Embedded Contact Homology
• A characterization of Zoll Riemannian metrics on the 2-sphere
• Slow volume growth for Reeb flows on spherizations and contact Bott–Samelson theorems
• Classification of the Actions of the Circle on 3-Manifolds
• From one Reeb orbit to two

This page was built for publication: The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed