Cohomologie de Dolbeault feuillet\'ee du feuilletage complexe affine de Reeb

Let $\mathcal{F}$ be a complex affine Reeb foliation of dimension $1$ on the Hopf manifold ${\mathbb{S}}^{n+1}\times {\mathbb{S}}^1$. We prove that its foliated Dolbeault cohomology in degree $1$ is isomorphic to $\mathbb{C}$ by giving an explicit generator.