Flat surfaces along swallowtails

Abstract

We consider developable surfaces along the singular set of a swallowtail which are considered to be flat approximations of the swallowtail. For the study of singularities of such developable surfaces, we introduce the notion of Darboux frames along swallowtails and invariants. As a by-product, we give a new example of a frontal which is locally homeomorphic to a swallowtail.