Bertrand Curves of AW(k)-Type in the Equiform Geometry of the Galilean Space

Abstract

We consider curves of AW($k$)-type ($1\le k\le 3$) in the equiform geometry of the Galilean space $G_3$. We give curvature conditions of curves of AW($k$)-type. Furthermore, we investigate Bertrand curves in the equiform geometry of $G_3$. We have shown that Bertrand curve in the equiform geometry of $G_3$ is a circular helix. Besides, considering AW($k$)-type curves, we show that there are Bertrand curves of weak AW(2)-type and AW(3)-type. But, there are no such Bertrand curves of weak AW(3)-type and AW(2)-type.