In this paper, we consider a time-like sweeping surface and its local singularities with Bishop frame in Minkowski 3-space E 1 3 . Subsequently, we derive the sufficient and necessary conditions for this surface to be spacelike developable ruled surface. In particular, we mainly focus on the study for the resulting spacelike developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding spacelike developable surfaces.

In this paper, we attain the problem of constructing hypersurfaces from a given geodesic curve in 4D Euclidean space E4. Using the Serret–Frenet frame of the given geodesic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be geodesic. We illustrate this method by presenting some examples.