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

Rafael López, Esma Demir

Published 2010-06-11, updated 2010-06-14Version 2

In this work we find all helicoidal 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 show that the only possibility is that the axis is spacelike and the center of the circle lies in the axis.