  For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is
known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if
and only if the (tautness) class defined by the mean curvature form
$\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the
transversally orientable case, tautness is equivalent to the non-vanishing of
the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where $n = \codim
\mathcal{F}$. By the Poincar\'e Duality, this last condition is equivalent to
the non-vanishing of the basic twisted cohomology group
$H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is
not compact, the tautness class is not even defined in general. In this work,
we recover the previous study and results for a particular case of riemannian
foliations on non compact manifolds: the regular part of a singular riemannian
foliation on a compact manifold (CERF).
