  We observe that the class of metric $f$-$K$-contact manifolds, which
naturally contains that of $K$-contact manifolds, is closed under forming
mapping tori of automorphisms of the structure. We show that the de Rham
cohomology of compact metric $f$-$K$-contact manifolds naturally splits off an
exterior algebra, and relate the closed leaves of the characteristic foliation
to its basic cohomology.
