# Normal curves on a smooth immersed surface

## TL;DR

This paper investigates conditions under which a normal curve on a smooth immersed surface remains invariant under isometry, analyzing deviations in tangential and normal components.

## Contribution

It provides new sufficient conditions for the invariance of normal curves under isometry and quantifies deviations in their components.

## Key findings

- Identifies conditions for normal curve invariance under isometry
- Quantifies deviations of tangential and normal components
- Enhances understanding of surface geometry transformations

## Abstract

The aim of this paper is to investigate the sufficient condition for the invariance of a normal curve on a smooth immersed surface under isometry. We also find the the deviations of the tangential and normal components of the curve with respect to the given isometry.