# Natural mates of non-null Frenet curves in Minkowski 3-space

## TL;DR

This paper introduces the concept of natural mates for non-null Frenet curves in Minkowski 3-space and explores their geometric relationships and conditions for special curve types.

## Contribution

It defines natural mates for non-null Frenet curves in Minkowski 3-space and establishes conditions for these mates to be special curves like slant helices or spherical.

## Key findings

- Conditions for natural mates to be slant helices
- Criteria for natural mates to be spherical curves
- Characterization of curves with constant curvature

## Abstract

In this paper, we give the definition of the natural mate of a non-null Frenet curve in Minkowski 3-spaces. The main purpose of this paper is to prove some relationships between a non-null Frenet curve and its natural mate. In particular, we obtain some necessary and suffcient conditions for the natural mate of a non-null Frenet curve to be a slant helix, a spherical curve, or a curve of constant curvature. Several applications of our main results are also presented.