Some Characterizations of Euler Spirals in E_1^{3}

TL;DR

This paper characterizes Euler spirals in three-dimensional Minkowski space, exploring their properties and relationships with Bertrand curves and helices to deepen understanding in differential geometry.

Contribution

It introduces new characterizations of Euler spirals in E_1^{3} based on their linear curvature property and examines their connections with other special curves.

Findings

Euler spirals have linear curvature properties.

Relationships between Euler spirals, Bertrand curves, and helices are established.

The approach enhances understanding of Euler spirals in differential geometry.

Abstract

In this study, some characterizations of Euler spirals in E_1^{3} have been presented by using their main property that their curvatures are linear. Moreover, discussing some properties of Bertrand curves and helices, the relationship between these special curves in E_1^{3} have been investigated with different theorems and examples. The approach we used in this paper is useful in understanding the role of Euler spirals in E_1^{3} in differential geometry.