Quaternionic Shape Operator

Characterizations of Unit Darboux Ruled Surface with Quaternions

“…Theorem 2.1. [11] Let M be a surface with parameter u and β(u) be a unit speed curve in M . Using the quaternion operator…”

“…Then, we can say that the vector Q(u) × ⃗ T (u) is obtained by revolving ⃗ T (u) around the normal vector ⃗ Z(u) of the surface through twice the angle of φ [11].…”

“…Aslan and Yaylı have defined the quaternionic shape operator by the quaternion. Their article has aimed to find a way to the invariants of the surface using Darboux frames and quaternions [11]. In [12,13], the connection between split quaternions and surfaces with the constant slope in Minkowski 3-space has been explored.…”

Motions on curves and surfaces using geometric algebra

“…Some results have been achieved about these surfaces using quaternions. Also, using quaternions in the shape operator expressed by Darboux frame, we defined the quaternionic shape operator [16]. Moreover, we used the quaternionic shape operator in researching of the differential properties of surfaces.…”

Quaternionic and Dual Quaternionic Darboux Ruled Surfaces

“…The invariants (shape operator, Gauss curvature, etc.) of surfaces are expressed quaternionically [1,2]. Ruled surfaces are examined in both Euclidean space and dual space and some important results are given [4,14].…”