# Rectifying curves under conformal transformation

## TL;DR

This paper explores how rectifying curves behave under conformal transformations, identifying conditions for invariance and demonstrating that certain properties like normal component and geodesic curvature are preserved.

## Contribution

It provides a sufficient condition for rectifying curves to remain conformally invariant and shows specific invariants under such transformations.

## Key findings

- Normal component of rectifying curves is homothetic invariant.
- Geodesic curvature remains invariant under conformal transformation.
- Identifies conditions for conformal invariance of rectifying curves.

## Abstract

The main aim of this paper is to investigate the nature of invariancy of rectifying curve under conformal transformation and obtain a sufficient condition for which such a curve remains conformally invariant. It is shown that the normal component and the geodesic curvature of the rectifying curve is homothetic invariant.