Ricci Curvature, Reeb Flows and Contact 3-Manifolds
arXiv:1911.11109 · doi:10.1007/s12220-021-00665-6
Abstract
Given a contact 3-manifold we consider the problem of when a given function can be realized as the Ricci curvature of a Reeb vector field for the contact structure. We will use topological tools to show that every admissible function can be realized as such Ricci curvature for a singular metric which is an honest compatible metric away from a measure zero set. However, we will see that resolving such singularities depends on contact topological data and is yet to be fully understood.
arXiv comment23 pages, 3 figures. We welcome any comments
References in corpus (10)
- Géométrie de contact: de la dimension trois vers les dimensions supérieures
- The Weinstein conjecture for stable Hamiltonian structures
- Tightness in contact metric 3-manifolds
- Resolution of symplectic cyclic orbifold singularities
- The Completion of the Manifold of Riemannian Metrics with Respect to its Metric
- Geodesible contact structures on 3--manifolds
- Dynamics and Topology of Conformally Anosov Contact 3-Manifolds
- Quantitative Darboux theorems in contact geometry
- Introductory Lectures on Contact Geometry
- 1/4-Pinched Contact Sphere Theorem