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

Abstract

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