In this paper, we give the parametric equation of Bishop frame for a timelike sweeping surface with unit speed curve in Minkowski 3-space. We introduce new geometric invariant to explain properties and local singularities surface. derive sufficient necessary conditions be developable ruled Afterwards, take advantage singularity theory classification Furthermore, some representative examples sho...

In this paper, we analyze involutes of pseudo-null curves in Lorentz–Minkowski 3-space. Pseudo-null are spacelike with null principal normals, and their can be defined analogously as for the Euclidean curves, but they exhibit properties that cannot occur space. The first result paper is more precisely, straight lines. Furthermore, a method reconstruction curve from given line its involute provi...