Null generalized helices in $L^3$ and $L^4$, 3 and 4-dimensional Lorentzian space

Abstract

In this paper we obtain the harmonic curvatures of a null generalized helix in $L^3$ and $L^4$, 3 and 4-dimensional Lorentzian spaces. Thus we another definitions of null generalized helix in terms of harmonic curvatures. Also we find the relation of between Frenet frame, slope axis and curvature functions $k_1$, $k_2$ of null generalized helix. Finally we characterize the null helices thanks to harmonic curvatures in $L^3$ and $L^4$, 3 and 4- dimensional Lorentzian space.