Ruled surfaces in Minkowski 3-space and split quaternion operators (Q2052884)

This article is a direct extension of [\textit{S. Aslan} et al., J. Geom. Phys. 161, Article ID 104048, 10 p. (2021; Zbl 1460.53004)]. Similar to the techniques given in [loc. cit.], here the authors define an operator, called split quaternion operator \(Q(s, t) = s + u(t)\). Here \(s\) be a real variable and \(u(t)\) is a curve in the Lorentz Minkowski space \(\mathbb E_1^3\). The authors classify this operator into three types based on the norm of the quaternion. Let \(w(t)\) be the curve on the Lorentzian unit sphere or on the hyperbolic unit sphere, then one of the results in the article says that the split quaternion product of the split quaternion operator \(Q(s, t)\) and the pure split quaternion \(w(t)\) yields a ruled surface in \(\mathbb E_1^3\) if the position vector of the spherical curve \(w(t)\) is perpendicular to the vector part of the operator \(Q(s, t)\).