The Geometric Invariants of Null Cartan Curves Under The Similarity Transformations

TL;DR

This paper investigates the differential geometry of null Cartan curves in Minkowski space-time under similarity transformations, extending the fundamental theorem and characterizing self-similar null curves through shape Cartan curvatures.

Contribution

It introduces the fundamental theorem for null Cartan curves under similarity motions and derives equations for all self-similar null curves based on shape Cartan curvatures.

Findings

Extended the fundamental theorem for null Cartan curves under similarity transformations

Derived equations characterizing all self-similar null curves

Provided a classification of null Cartan curves based on shape Cartan curvatures

Abstract

In this paper, we study the differential geometry of null Cartan curves under the similarity transformations in the Minkowski space-time. Besides, we extend the fundamental theorem for a null Cartan curve according to a similarity motion. We find the equations of all self-similar null curves which is given its shape Cartan curvatures.