Helicoidal surfaces with constant mean curvature

Abstract

We describe the space ∑H of all surfaces in R3 that have constant mean curvature H≠0 and are invariant by helicoidal motions, with a fixed axis, of R3. Similar to the case ∑0 of minimal surfaces ∑H behaves roughly like a circular cylinder where a certain generator corresponds to the rotation surfaces and each parallel corresponds to a periodic family of isometric helicoidal surfaces. © 1982 Tohoku Mathematical Journal.