The dual spatial quaternionic expression of ruled surfaces

Abstract

In this paper, the ruled surface which corresponds to a curve on dual unit sphere is rederived with the help of dual spatial quaternions. We extend the term of dual expression of ruled surface using dual spatial quaternionic method. The correspondences in dual space of closed ruled surfaces are quaternionically expressed. As a consequence, the integral invariants of these surfaces and the relationships between these invariants are shown.

Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces

“…Moreover, some special curves of the partner ruled surfaces are characterized [14]. Şenyurt and Çalışkan examine ruled surfaces as dual quaternions and explain the characterization of this surface [15]. Aslan and Yaylı define the quaternionic shape operator expressed in the surface.…”

“…He categorizes the ruled and the translation surfaces [19]. Some authors give crucial results about the curves and surfaces in different spaces [12,15,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. We can find more motivations of our work from some articles (see [38][39][40][41][42][43][44][45][46][47][48][49][50]).…”

Characterizations of Unit Darboux Ruled Surface with Quaternions

“…In [7], the authors have expressed the ruled surface as quaternionic and computed some properties of the ruled surface. Moreover, they have investigated the dual ruled surface using dual quaternion [8]. In light of these studies, C ¸alışkan have examined the quaternionic and dual quaternionic Darboux ruled surfaces [9].…”