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

Abstract

We consider curves of AW(k)-type (1≤k≤3) in the equiform geometry of the Galilean space G3. We give curvature conditions of curves of AW(k)-type. Furthermore, we investigate Bertrand curves in the equiform geometry of G3. We have shown that Bertrand curve in the equiform geometry of G3 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.