Ruled Surfaces in Minkowski 3-space and Split Quaternion Operators

Aslan S., BEKAR M., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.31, no.5, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1007/s00006-021-01176-x
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Keywords: Split quaternions, Ruled surfaces, Minkowski 3-space, Spherical curves in Minkowski 3-space, 2-parameter homothetic motions, ROTATIONS
  • Gazi University Affiliated: Yes

Abstract

In this paper, we define and classify split quaternion operators. Then, we show that the split quaternion product of a split quaternion operator and a curve, which lies on Lorentzian unit sphere or on hyperbolic unit sphere, parametrizes a ruled surface in the 3-dimensional Minkowski space E-1(3) if the vector part of the operator is perpendicular to the position vector of the spherical curve. Moreover, the ruled surfaces are represented as 2-parameter homothetic motions in E-1(3) by using semi-orthogonal matrices corresponding to the split quaternion operators. Finally, some examples are given to illustrate some applications of our main results.