Helicoidal surfaces under the cubic screw motion in Minkowski 3-space

Abstract

In this paper, we construct helicoidal surfaces under the cubic screw motion with prescribed mean or Gauss curvature in Minkowski 3-space E 1 3 . We also find explicitly the relation between the mean curvature and Gauss curvature of them. Furthermore, we discuss helicoidal surfaces under the cubic screw motion with H 2 = K and prove that these surfaces have equal constant principal curvatures.