A New Method for Designing Involute Trajectory Timelike Ruled Surfaces in Minkowski 3-Space

Abstract

In this study, we present the new concept of involute trajectory ruled surface in Minkowski 3-space. The involute trajectory timelike ruled surface is a surface generated by the motion of a timelike oriented line X along the spacelike involute curve γ (s) of a given timelike base curve r (s). The main purpose of this article is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. These surfaces are formed depending on the angle θ between the Darboux vector D and the binormal vector b of the evolute curve r (s). Also, some new results and theorems related to the developability of the involute trajectory timelike ruled surfaces are obtained. Finally, we illustrate these surfaces by presenting one example. © Soc.