Some Parallel Surfaces in Three-Dimensional Minkowski Space as the Discriminant Set of a Certain Family of Functions

In this paper we prove that, in three-dimensional Minkowski space, the family of parallel surfaces to a given surface at a certain distance can be obtained as the discriminant set of a certain family of functions. As consequence, we obtain that Minkowski spheres with prescribed radius, having contact of order 1 with a surface, have the centers on the parallel surface at distance equal to the radius. We give an example showing that the parallel surface to a timelike flat surface admits cuspidal edge as singularity