Ruled surfaces constructed by quaternions

Aslan S., BEKAR M., Yaylı 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
  • Gazi Üniversitesi Adresli: Evet

Özet

© 2020 Elsevier B.V.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 R3. We prove that quaternion product of this operator and a spherical curve represents a ruled surface in R3 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 R3 can be obtained by this operator. Finally, we give the geometric interpretations of these operators with some examples.