Singularity Classification Of Rectifying Developables Surfaces

In this paper,we investigate the singularities of rectifying developable and tangentail Darboux developable generated by framed curve in Lorentz-Minkowski3-space,a Frenet-Serret type formula and four important invariants associated with framed curve .Using the classification approaches of the finite type on the tangent developables and defining the extended striction curve,this paper gives the detailed classification of the rectifying developable and tangentail Darboux developable of singular curves.It is demonstrated that the rectifying developable and tangentail Darboux developable of singular curves will appear not only in cuspidal edge and swallowtail,but cuspidal beaks and cuspidal cross-cap under suitable conditions.Especially the singularities of these two kinds of surfaces of singular curves are associated with curvature functions such that the singularities can be characterized by these functions.Three examples are provided to put the theoretical results into the practice of computation and classification.