Some characterizations of rectifying curves on a smooth surface in Euclidean 3-space

Abstract

In this paper, we investigate sufficient condition for the invariance of a rectifying curve on a smooth surface immersed in Euclidean 3-space under isometry by using Darboux frame {T, P,U}. Further, we find the deviations of the position vector of a rectifying curve on the smooth surface along any tangent vector T = aφu + bφv with respect to the isometry. We also find the deviations of the position vector of a rectifying curve on the smooth surface along the unit normal U to the surface and along P (= U × T ) with respect to the isometry. Mathematics Subject Classification 2020: 53A04, 53A05, 53A15.