Constructing surfaces with constant gaussian curvature along a given curve in the lie groups

In this study, surfaces with constant Gaussian curvature along a given curve in three-dimensional Lie groups, surfaces with constant Gaussian curvature passing trough the given Smarandache curves and surfaces with constant Gaussian curvature passing trough a given curve with respect to the alternative frame {N,C,W} are obtained. These surfaces are parametrically expressed as the linear combination of the Frenet vector elements and the marching-scale function of the given curves. Some examples of the data obtained in this study and are given visualized