Spherical Darboux images of curves on surfaces

Abstract

For a regular curve on a surface, we have a moving frame along the curve which is called the Darboux frame. We induce three special vector fields along the curve associated to the Darboux frame and investigate their singularities as an application of the theory of spherical dualities. Moreover, characterizations of isophotic curves on a surface are given by using one of the three special vector fields.