On Developable Surfaces with a Common Line of Curvature in Minkowski 3-Space \(E_{1}^{3}\)

In this paper we study the problem of constructing a spacelike and timelike developable surface family from a given non-null curve as a common line of curvature in Minkowski 3-space \(E_{1}^{3}\). The necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface are also analyzed. Some representative curves are chosen to construct the corresponding developable surfaces which possess these curves as lines of curvature. Finally, we have illustrated the convenience and efficiency of this approach by some representative examples.