Motion groups and circular helices in Lorentz 3-space

Abstract

In this paper, we find the curves which are orbits of of points under the homothetic and helicoidal motion groups in Lorentz 3-space. Also, we show that if these curves are Frenet curves then their curvature and torsion are constant. So we can say that these curves are circular helix in Lorentz 3-space.