#### Volume 8, issue 3 (2008)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
The curvature of contact structures on $3$–manifolds

Algebraic & Geometric Topology 8 (2008) 1567–1579
##### 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.

##### Keywords
contact structure, uniformization, curvature
Primary: 53D35
Secondary: 53B21