Null Similar Curves with Variable Transformations in Minkowski 3-space

TL;DR

This paper introduces null similar curves in Minkowski 3-space, explores their properties, and establishes their relation to null Bertrand pairs, null geodesics, and null helices, highlighting their geometric significance.

Contribution

It defines null similar curves with variable transformations and characterizes their relationship to null Bertrand pairs, null geodesics, and null helices in Minkowski 3-space.

Findings

Null curves are null similar if and only if they form a null Bertrand pair.

Null geodesics and null helices are examples of null similar curves.

Properties of null similar curves are systematically derived.

Abstract

In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and null helices form the families of null similar curves with variable transformation.