On k-type spacelike slant helices lying on lightlike surfaces

Abstract

In this paper, we dene k-type spacelike slant helices lying on a lightlike surface in Minkowski 3-space 
according to their Darboux frame for k=0,1,2. We obtain the necessary and the sucient
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.