Surfaces with a common asymptotic curve in the 3D Galilean space 𝔾₃

In this study, we consider the problem of how to characterize a surface family from a given common asymptotic curve in a three-dimensional Galilean space [Formula: see text]. We obtain a parametrization of the surface such that the surface tangent plane is coincident with the curve osculating plane. The extension to ruled surfaces is also outlined. We illustrate this method by presenting some examples.