Vector fields on bifurcation diagrams of quasi singularities

We describe the generators of the vector fields tangent to the bifurcation diagrams and caustics of simple quasi boundary singularities. As an application, submersions on the pair $(G,B)$, which consists of a cuspidal edge $G$ in ${\mathbb{R}}^3$ that contains a distinguishing regular curve $B$, are classified. This classification was used as a means to investigate the contact that a general cuspidal edge $G$ equipped with a regular curve $B\subset G$ has with planes. The singularities of the height functions on $(G,B)$ are discussed and they are related to the curvatures and torsions of the distinguished curves on the cuspidal edge. In addition to this, the discriminants of the versal deformations of the submersions that were accomplished are described and they are related to the duality of the cuspidal edge.