A research on space-like Bertrand curve pair in 3D lightlike cone

Abstract

In this study, the W-Bertrand curves lying on the Q3 are examined and the notion of γ−Bertrand curves( and α−Bertrand curves, β−Bertrand curves, y−Bertrand curves, respectively). Also, the Bertrand pair {γ, Γ} in terms of their curvature functions are obtained, and the necessary and sufficient conditions for the W-Bertrand curves are expressed using the asymptotic orthonormal frame in Q3 . Furthermore, the helix curve is characterized in terms of curvature according to the condition of being W-Bertrand curve pair.