On Nonlightlike Curves in Minkowski Space-time

Abstract

In this paper, some special nonlightlike curves are investigated depending on characterizations of their Serret-Frenet frames in Minkowski space-time. Firstly, a great survey of nonlightlike curves in Minkowski space-time is stated. To generalize the results, the nonlightlike curves with the character of Serret-Frenet frame (ε₁,ε₂,ε₃,ε₄) are considered. So that, the necessary or/and sufficient conditions of a given nonlightlike curve to be a straight line, plane curve, helix and to lie on pseudohyperbolical space H₀³(r) and Lorentzian hypersphere S₀³(r) are stated both depending on curvature functions and character of Serret-Frenet frame of the curve, respectively.