Characterizations of rectifying curves under conformal transformation using Darboux frame in Euclidean 3-Space

This paper presents the study of rectifying curves on smooth surfaces using the Darboux frame in Euclidean-3 space. We obtain sufficient conditions for the image of an asymptotic and non-asymptotic rectifying curve to remain invariant under conformal transformation. Furthermore, we investigate the variations of these asymptotic and non-asymptotic rectifying curves along any tangent vector [Formula: see text], along the surface normal [Formula: see text], and along [Formula: see text].