The curvature of contact structures on 3–manifolds

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.