Ruled surfaces constructed by quaternions

Aslan S., BEKAR M., YAYLI Y.

JOURNAL OF GEOMETRY AND PHYSICS, cilt.161, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 161
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.geomphys.2020.104048
  • Dergi Adı: JOURNAL OF GEOMETRY AND PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Spherical curves, Ruled surfaces, Dual numbers, Quaternions, 2-parameter homothetic motions
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we define a quaternionic operator whose scalar part is a real parameter and vector part is a curve in three dimensional real vector space R-3. We prove that quaternion product of this operator and a spherical curve represents a ruled surface in R-3 if the vector part of the quaternionic operator is perpendicular to the position vector of the spherical curve. We express this surface as 2-parameter homothetic motion using the matrix representation of the operator. Furthermore, we define another quaternionic operator and show that each ruled surface in R-3 can be obtained by this operator. Finally, we give the geometric interpretations of these operators with some examples. (C) 2020 Elsevier B.V. All rights reserved.