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.