Equiform Differential Geometry of Curves in Minkowski Space-Time

TL;DR

This paper develops the equiform differential geometry framework for space and timelike curves in 4D Minkowski space, providing conditions and characterizations of special curves like helices based on their equiform curvatures.

Contribution

It introduces the equiform differential geometry of curves in Minkowski space and characterizes general helices using equiform curvatures, a novel approach in this context.

Findings

Conditions for space and timelike curves are derived.

General helices are characterized via equiform curvatures.

Framework extends differential geometry in Minkowski space.

Abstract

In this paper, we establish equiform differential geometry of space and timelike curves in 4-dimensional Minkowski space. We obtain some conditions for these curves. Also, general helices with respect to their equiform curvatures are characterized.