Slant Ruled Surfaces and Slant Developable Surfaces of Spacelike Curves in Lorentz-Minkowski $3$-space

Abstract

In this paper, by means of the Lorentzian Frenet frame along a spacelike curve in Lorentz-Minkowski 3-space, we construct slant ruled surfaces and slant developable surfaces with different director curves which belong to one-parameter families of the pseudo-spheres in this space. Moreover, for each slant ruled surface with each director curve, we search if this slant ruled surface has any singularities or not. Furthermore, for the cases in which the singularities appear, we determine the singularities of non-lightlike and non-cylindrical slant developable surfaces and also investigate the singularities of slant ruled surfaces.