In the present paper, we define a Bertrand curve in the three-dimensional Lie group G with a bi-invariant metric, and we show a Frenet curve α with Frenet curvatures k 1 and k 2 in G is a Bertrand curve if and only if it satisfies Ak 1 + B(k 2 +k 2) = 1, where A and B are some constants andk 2 = 1/2 [V 1 , V 2 ], V 3. Also, we investigate a Bertrand curve using the Frenet curvature conditions of AW(k)-type (k = 1, 2, 3) curves in G.

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G 1 3 . Also, we classify linear Weingarten rotational surfaces in G 1 3 . A linear Weingarten surface is the surface having a linear equation between the Gaussian curvature and the mean curvature of a surface. In last section, we construct isotropic rotational surfaces in G 1 3 with prescribed mean curvature given by smooth function. As the results, we classify isotropic rotational surfaces with constant mean curvature.Mathematics Subject Classification: 53A35, 53B30