  In this paper we establish a Gaffney type inequality, in $W^{\ell,p}$-Sobolev
spaces, for differential forms on sub-Riemannian contact manifolds without
boundary, having bounded geometry (hence, in particular, we have in mind
non-compact manifolds). Here $p\in]1,\infty[$ and $\ell=1,2$ depending on the
order of the differential form we are considering. The proof relies on the
structure of the Rumin's complex of differential forms in contact manifolds, on
a Sobolev-Gaffney inequality proved by Baldi-Franchi in the setting of the
Heisenberg groups and on some geometric properties that can be proved for
sub-Riemannian contact manifolds with bounded geometry.
