Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 8, Number 3 (2008), 1567-1579.
The curvature of contact structures on $3$–manifolds
We study the sectional curvature of plane distributions on –manifolds. We show that if a distribution is a contact structure it is easy to manipulate its curvature. As a corollary we obtain that for every transversally oriented contact structure on a closed –dimensional manifold, there is a metric such that the sectional curvature of the contact distribution is equal to . We also introduce the notion of Gaussian curvature of the plane distribution. For this notion of curvature we get similar results.
Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1567-1579.
Received: 4 February 2008
Revised: 24 July 2008
Accepted: 27 July 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Secondary: 53B21: Methods of Riemannian geometry
Krouglov, Vladimir. The curvature of contact structures on $3$–manifolds. Algebr. Geom. Topol. 8 (2008), no. 3, 1567--1579. doi:10.2140/agt.2008.8.1567. https://projecteuclid.org/euclid.agt/1513796897