  Haefliger cohomology characterizes taut foliated manifolds by Haefliger's
theorem. We show that Haefliger cohomology characterizes strongly tense
foliated manifolds, namely, foliated manifolds which admit a Riemannian metric
such that the mean curvature form of the leaves is closed and basic. We show
that Haefliger cohomology is dual to invariant cohomology for complete
Riemannian foliations. As an application of these results, we prove that any
complete Riemannian foliation is strongly tense, which is a generalization of
Dom\'{i}nguez's tenseness theorem for Riemannian foliations on closed
manifolds.
