Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Abstract

We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis. © 2014 Versita Warsaw and Springer-Verlag Wien.