Bertrand curves of AW(k)-type in Lorentzian space

Abstract

In this study, firstly, we give curvature conditions of AW(k)-type ( 1 ≤ k ≤ 3 ) curves. Then considering AW(k)-type curves, we investigate Bertrand curves γ : I → L 3 with κ 1 ( s ) ≠ 0 and κ 2 ( s ) ≠ 0 . We show that there are Bertrand curves of AW(1)-type and AW(3)-type. Moreover, we study weak AW(2)-type and AW(3)-type conical geodesic curves in L 3 .