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2008 The curvature of contact structures on $3$–manifolds
Vladimir Krouglov
Algebr. Geom. Topol. 8(3): 1567-1579 (2008). DOI: 10.2140/agt.2008.8.1567

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.

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Vladimir Krouglov. "The curvature of contact structures on $3$–manifolds." Algebr. Geom. Topol. 8 (3) 1567 - 1579, 2008. https://doi.org/10.2140/agt.2008.8.1567

Information

Received: 4 February 2008; Revised: 24 July 2008; Accepted: 27 July 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1146.53025
MathSciNet: MR2443254
Digital Object Identifier: 10.2140/agt.2008.8.1567

Subjects:
Primary: 53D35
Secondary: 53B21

Rights: Copyright © 2008 Mathematical Sciences Publishers

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