Ruled surfaces constructed by quaternions


Aslan S., BEKAR M. , Yaylı Y.

Journal of Geometry and Physics, vol.161, 2021 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 161
  • Publication Date: 2021
  • Doi Number: 10.1016/j.geomphys.2020.104048
  • Title of Journal : Journal of Geometry and Physics

Abstract

© 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.