Bertrand curves of AW(k)-type in three dimensional Lie groups

Abstract

In this paper, we consider curves of AW(k)-type (1 ≤ k ≤ 3) in Three Dimensional Lie Groups. We give harmonic curvature conditions of AW(k)-type curves. Furthermore, we investigate that under what conditions AW(k)-type curves are helix. Besides, considering AW(k)-type curves, we investigate Bertrand curves and we show that there are Bertrand curves of AW(2), AW(3) and weak AW(2)−types.