Symplectic Asphericity, Category Weight, and Closed Characteristics of K-Contact Manifolds

Let $M$ be a closed K-contact $(2n+1)$-manifold equipped with a quasi-regular K-contact structure. Rukimbira proved that the Reeb vector field $\xi$ of this structure has at least $n+1$ closed characteristics. We note that $\xi$ has at least $2n+1$ closed characteristics provided that the space of leaves of the foliation determined by $\xi$ is symplectically aspherical.