A new characterization between osculating strip curves and ruled surfaces in Lorentzian space

Abstract

In this work, we study the conditions between osculating strip curves and ruled surfaces in Lorentzian space. For this study, we establish a system of differential equations characterizing both spacelike and timelike ruled surfaces in Lorentzian space by using the invariant quantities of osculating strip curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of relations between osculating strip curves and ruled surfaces in Lorentzian space.