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.

In Math. Meth. Appl. Sci.