# Geometric invariants of normal curves under conformal transformation in $\mathbb{E}^3$

## TL;DR

This paper studies how normal curves on surfaces in three-dimensional space behave under conformal transformations, identifying invariants and deviations, and generalizing previous results.

## Contribution

It provides new invariant conditions for normal curves under conformal maps and extends prior results as special cases.

## Key findings

- Derived invariant-sufficient conditions for conformal images of normal curves.
- Analyzed deviations of normal and tangential components under conformal transformations.
- Generalized earlier results to broader classes of transformations.

## Abstract

In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also find the deviations of normal and tangential components of the normal curve under the same motion. The results in \cite{9} are claimed as special cases of this paper.