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


TUNCER O. O.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7866
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Keywords: pseudo-Galilean space, generalized tube surface, Gaussian curvature, mean curvature, split semi-quaternion, magnetic flux tube, CANAL SURFACES, TUBULAR SURFACES, REAL

Abstract

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.