On the theory of fronts on the 2-sphere and the theory of space curves

Abstract

We apply the singularity theory of caustics and wave fronts on the 2-sphere and the theory of Legendrian curves of the (contact) manifold ST*\({\mathbb{S}}\)2 ∼ ℝP3 (consisting of tangent contact elements of the sphere\( {\mathbb{S}} \)2) to obtain new results in the theory of curves in the Euclidean 3-space. In this way, the singularity theory of caustics and wave fronts provides a new insight to the differential geometry of curves in the Euclidean 3-space.