Cohomologie feuilletée du flot affine de Reeb sur la variété de Hopf \({\Bbb S}^n\times {\Bbb S}^1\)

We determine explicitly the foliated cohomology \(H_{\cal F}^\ast (M)\) of the affine Reeb flow \({\cal F}\) on the Hopf manifold \({\Bbb S}^n\times {\Bbb S}^1\). The vector space \(H_{\cal F}^1(M)\) contains exactly the obstructions to solve the cohomological equation \(X\cdot f=g\) where \(f\) and \(g\) are \(C^\infty \)-functions and \(X\) is any non singular vector field defining the foliation \({\cal F}\). The topological dual of \(H_{\cal F}^1(M)\) is the space of distributions invariant by \(X\).