Curves with normal planes at constant distance from a fixed point

TL;DR

This paper studies special curves in 3D space where all normal planes are equally distant from a fixed point, providing characterizations of such curves.

Contribution

It introduces new characterizations of curves with normal planes at constant distance from a fixed point in Euclidean space.

Findings

Characterization of these curves in Euclidean space

Conditions for normal planes to be equidistant from a fixed point

Geometric properties of the curves

Abstract

We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.