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 $\left\{T,P,U\right\}$. Further, we find the deviations of the position vector of a rectifying curve on the smooth surface along any tangent vector $T=a{\varphi }_u+b{\varphi }_v$ 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 $P(=U\times T)$ with respect to the isometry.