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

Abstract

We study the geometry of non-minimal surfaces of supercritical constant mean curvature invariant under screw motions in the homogeneous 3-manifolds $\mathbb{E}(\kappa ,\tau )$ including the space-forms of non-negative curvature. We give a complete classification, thereby unifying and extending various previous results. We give the first classification for the Berger sphere case, and we exhibit a new family of screw motion CMC surfaces, called tubes.

References in corpus (3)

• Horizontal Delaunay surfaces with constant mean curvature in ${\mathbb{S}}^2\times \mathbb{R}$ and ${\mathbb{H}}^2\times \mathbb{R}$
• Invariant constant mean curvature tubes around a horizontal geodesic in $\mathbb{E}(\kappa ,\tau )$-spaces
• Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves