Quaternionic Approach of Slant Ruled Surfaces

Karaca E.

Advances in Applied Clifford Algebras, vol.32, no.4, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1007/s00006-022-01225-z
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Keywords: 2-Parameter homothetic motions, Dual numbers, Quaternions, Slant ruled surfaces
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.In this study, we show that the quaternion product of quaternionic operator whose scalar part is a real parameter and vector part is a curve in R3 and a spherical striction curve represents a slant ruled surface in R3 if the vector part of the quaternionic operator is perpendicular to the position vector of the spherical striction curve. In R3, exploitting this operator, we define the slant ruled surface corresponding to the natural lift curve on the subset of the tangent bundle of unit 2-sphere, TM¯. Then, we classify q¯ → - , h¯ → - and a¯ → - slant ruled surfaces. Furthermore, these surfaces can also be expressed with 2- parameter homothetic motions. Finally, we give the geometric interpretations of this operator with some examples.