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