On k-type spacelike slant helices lying on lightlike surfaces

Abstract

© University of Nis. All rights reserved. In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E3 according to their Darboux frame for k ∈ {0, 1, 2}. We obtain the necessary and the sufficient 1 conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geodesic torsion. Finally, we give some examples.