A Geometric View on the Surfaces of Rotation Generated by Killing Vector Field in Galilean 3-Space

In this paper, by using rotational matrix which is the subgroups of the manifold \(M\) corresponding to rotation, some certain results of describing the surface are given in detail obtaining Killing vector field in \(G_3\), the rotational surfaces generated by the rotational matrices are given using an isotropic curve and isotropic matrices of rotation in \(G_3\). Moreover, taking the Gaussian and mean curvatures of this special rotational surface, the conditions being linear Weingarten surfaces and \(HK\)-quadric surface are expressed harmonic surface.