Generalized tubes in pseudo-Galilean 3-space: Split semi-quaternionic representations and an application to magnetic flux tubes

This paper deals with generalized tube surfaces (GTs) and their geometric properties in pseudo-Galilean 3-space. We classify these surfaces into two types. We firstly compute the first and second fundamental forms to investigate geometric properties of a GT. Then, we obtain the condition for such a surface to be minimal and present some results which express the conditions for which parameter curves on a GT are geodesics, asymptotics, or lines of curvature. Furthermore, we show how to form GTs by using split semi-quaternions or their matrix representations. Finally, as an application, we introduce generalized magnetic flux tubes in pseudo-Galilean 3-space and obtain the local magnetic field components of such surfaces. The theory studied in the paper is supported by illustrated examples.

Automated summary

This paper discusses the geometric properties of generalized tube surfaces in pseudo-Galilean 3-space, including classification, conditions for minimal surfaces, characteristics of parameter curves, and formation using split semi-quaternions. It also introduces applications of generalized magnetic flux tubes in the space.