Singularities of parallels to tangent developable surfaces

Abstract

A tangent developable surface is defined as a ruled developable surface by tangent lines to a space curve and it has singularities at least along the space curve, called the directrix or the edge of regression. The class of tangent developable surfaces is invariant under the parallel deformations. In this paper the notions of tangent developable surfaces and their parallels are naturally generalised for frontal curves in general in Euclidean spaces of arbitrary dimensions. The singularities appearing on parallels to tangent developable surfaces of frontal curves are studied and the classification of generic singularities on them for frontal curves in 3 or 4 dimensional Euclidean spaces are given.