Rectifying curves on a smooth surface immersed in the euclidean space

TL;DR

This paper investigates conditions under which rectifying curves on smooth surfaces in Euclidean space remain unchanged under surface isometries, focusing on the invariance of their position vector components along surface normals.

Contribution

It provides a sufficient condition for rectifying curves to be invariant under surface isometries and analyzes the invariance of their normal components.

Findings

Rectifying curves are invariant under certain surface isometries.

The normal component of the position vector of rectifying curves remains invariant under these isometries.

The paper establishes a link between surface isometries and rectifying curve properties.

Abstract

The main objective of the present paper is to investigate a sufficient condition for which a rectifying curve on a smooth surface remains invariant under isometry of surfaces, and also it is shown that under such an isometry the component of the position vector of a rectifying curve on a smooth surface along the normal to the surface is invariant.