A study on special curves of AW(k)-type in the pseudo-Galilean space

TL;DR

This paper investigates special types of AW(k)-type curves within the pseudo-Galilean space, focusing on their geometric properties, classifications, and relationships between their curvatures, supported by examples and visualizations.

Contribution

It introduces classifications of equiform Bertrand curves as circular helices or isotropic circles and explores AW(3) and weak AW(3)-type curves in pseudo-Galilean space.

Findings

Equiform Bertrand curves are circular helices or isotropic circles.

Existence of equiform Bertrand curves of AW(3) and weak AW(3)-types.

Relations between the equiform curvatures of these curves.

Abstract

This paper is devoted to the study of AW(k)-type curves according to the equiform differential geometry of the pseudo-Galilean space. We show that equiform Bertrand curves are circular helices or isotropic circles of the pseudo-Galilean space. Also, there are equiform Bertrand curves of AW(3) and weak AW(3)-types. Moreover, we give the relations between the equiform curvatures of these curves. Finally, examples of some special curves are given and plotted.