Curvature of the contact distribution

摘要

We define and study both the sectional and φ-sectional curvatures of the contact distribution D on a K-contact manifold M. We prove that 3-dimensional K-contact manifolds of constant curvature are the only ones who carry contact distributions of constant curvature. Also, we prove that D is of constant φ-sectional curvature if and only if M is a Sasakian space form.