On k-type null Cartan slant helices in Minkowski 3-space

Abstract

© 2018 John Wiley & Sons, Ltd. In this paper, we define k-type null Cartan slant helices lying on a timelike surface in Minkowski space E 31 according to their Darboux frame, where k ε {0, 1, 2}.We study these helices by using their geodesic curvature, normal curvature, and geodesic torsion. Additionally, we determine their axes and consider the special cases when the mentioned helices are geodesic curves and principal curvature lines lying on the timelike surface in E 31 . Furthermore,we obtain some interesting relations between 0-, 1-, and 2-type null Cartan slant helices.