On the involutes of a regular curve according to lightcone frame

Abstract

In this study, we introduce a new defnition of the involute curve e of a regular curve in Minkowski 3-space using the lightcone frame. First, we determine the distance between the involute-evolute pair with respect to the lightcone frame. Then, we derive the Frenet apparatus of the involute curve e and establish the necessary condition for e to be the involute of . Finally, to enhance understanding, we illustrate the proposed method with a representative example.