On characterizations of general helices for ruled surfaces in the pseudo-Galilean space G13-(Part-I)

Abstract

T. Ikawa obtained in [5] the following characteristic ordinary differential equation del x del x del x X - Kdel x X = 0 K = k(2) - tau(2) for the circular helix which corresponds to the case that the curvatures k and tau of a time-like curve a on the Lorentzian manifold M are constant. N. Ekmekci and H. H. Hacisalihoglu generalized in [4] T. Ikawa's this result, i.e., k and T are variable, but is constant. In [1] H. Balgetir, M. Bektas and M. Ergut obtained a geometric characterization of null Frenet curve with constant ratio of curvature and torsion (called null general helix). In this paper, making use of method in [1, 4, 5], we obtained characterizations of a curve with respect to the frenet frame of ruled surfaces in the 3-dimensional pseudo-Galilean space G(3)(1).