In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E 3 1 according to their Darboux frame for k ∈ {0, 1, 2}. We obtain the necessary and the sufficient 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.

In this paper, we introduce T-slant, N-slant and B-slant helices in the pseudo-Galilean space G13 and define an angle between the spacelike and the timelike isotropic vector lying in the pseudo-Euclidean plane x = 0. In particular, we obtain the explicit parameter equations of the T-slant helices and prove that there are no N-slant and B-slant helices in G13. We also prove that there are no Darboux helices in the same space.