Similar and Self-similar Curves in Minkowski n-space

TL;DR

This paper explores the properties of non-null curves in Minkowski n-space under similarity transformations, identifying invariants, extending fundamental theorems, and classifying all self-similar curves.

Contribution

It introduces a comprehensive analysis of similarity invariants and classifies all non-null self-similar curves in Minkowski n-space, extending existing geometric theories.

Findings

Identified geometric invariants of non-null curves under similarity transformations.

Extended the fundamental theorem for non-null curves in Minkowski space.

Classified all non-null self-similar curves in Minkowski n-space.

Abstract

In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion. We determine all non-null self-similar curves in the Minkowski n-space.