Classications of special curves in the three-dimensional lie group

Abstract

In the present paper, we dene a Bertrand curve in the three-dimensional Lie group G with a bi-invariant metric, and we show a Frenet curve with Frenet curvatures k1 and k2 in G is a Bertrand curve if and only if it satises Ak1 + B(k2 + k2) = 1, where A and B are some constants and k2 = 1=2h[V1; V2]; V3i. Also, we investigate a Bertrand curve using the Frenet curvature conditions of AW(k)-type (k = 1; 2; 3) curves in G. ? 2016 Chul Woo Lee and Jae Won Lee.