Screw motion surfaces of constant mean curvature in homogeneous 3-manifolds

We study the geometric behavior of constant mean curvature surfaces invariant under screw motion in the homogeneous 3-manifolds $\mathbb{E}(\kappa,\tau)$ as well as the space-forms of non-negative curvature and give a complete classification. We give a unified presentation of results that have appeared in the literature in various forms