Ricci Curvature, Reeb Flows and Contact 3-Manifolds
Differential Geometry
2021-04-20 v1 Geometric Topology
Symplectic Geometry
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.
Cite
@article{arxiv.1911.11109,
title = {Ricci Curvature, Reeb Flows and Contact 3-Manifolds},
author = {Surena Hozoori},
journal= {arXiv preprint arXiv:1911.11109},
year = {2021}
}
Comments
23 pages, 3 figures. We welcome any comments