Ruled Surfaces in Minkowski 3-space and Split Quaternion Operators

Aslan S., BEKAR M., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.31, sa.5, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00006-021-01176-x
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Anahtar Kelimeler: Split quaternions, Ruled surfaces, Minkowski 3-space, Spherical curves in Minkowski 3-space, 2-parameter homothetic motions, ROTATIONS
  • Gazi Üniversitesi Adresli: Evet

Özet

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.