On T-slant, N-slant and B-slant Helices in Pseudo-Galilean Space G^1_3

Abstract

In this paper, we redene the notion of the general helices in pseudo-Galilean space G_1^3 and introduce a k-type slant helices for k=0,1,2. We characterize the 0-type slant helices in terms of their curvature functions and obtain their explicit parameter equations. In particular, we prove that there are
no 1-type and 2-type slant helices. We introduce Darboux helices in G13
and show that the 0-type slant helices with an isotropic axis are Darboux helices with zero torsion. Finally, we prove that the 0-type
slant helices with an isotropic axis, whose curvature is a linear function in arc-length parameter x, are the curves of the constant precession and give some examples.