The Similarity Invariants of non-lightlike Frenet curves in the Minkowski 3-space

TL;DR

This paper investigates the differential geometric invariants of non-lightlike curves in Minkowski 3-space under similarity transformations, extending the fundamental theorem for such curves within this geometric context.

Contribution

It introduces the similarity transformation group in Minkowski 3-space and extends the fundamental theorem for non-lightlike curves considering these transformations.

Findings

Describes invariants of non-lightlike curves under similarity transformations

Extends the fundamental theorem for these curves in Minkowski 3-space

Provides a framework for understanding curve invariants in Minkowski geometry

Abstract

In this paper, we firstly introduce the group of similarity transformations in the Minkowski-3 space. We describe differential- geometric invariants of a non-lightlike curve according to the group of similarity transformations of the Minkowski 3-space. We show extension of fundamental theorem for non-lightlike curves under the group of similarity of the Minkowski 3-space.