Algebraic & Geometric Topology

The curvature of contact structures on $3$–manifolds

Vladimir Krouglov

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Abstract

We study the sectional curvature of plane distributions on 3–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 3–dimensional manifold, there is a metric such that the sectional curvature of the contact distribution is equal to 1. We also introduce the notion of Gaussian curvature of the plane distribution. For this notion of curvature we get similar results.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1567-1579.

Dates
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
https://projecteuclid.org/euclid.agt/1513796897

Digital Object Identifier
doi:10.2140/agt.2008.8.1567

Mathematical Reviews number (MathSciNet)
MR2443254

Zentralblatt MATH identifier
1146.53025

Subjects
Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Secondary: 53B21: Methods of Riemannian geometry

Keywords
contact structure uniformization curvature

Citation

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


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