In this paper, we investigate spacelike and timelike canal surfaces foliated by S12 pseudo spheres in Minkowski 3-space based on the Bishop frame. Various types of canal surfaces, including Weingarten, linear Weingarten, developable, and minimal forms, are categorized to highlight the singular points and the geometric properties of such surfaces. Our analysis sheds light on the intrinsic properties of these surfaces and contributes to the understanding of their behavior within the context of Minkowski geometry. Finally, we present a computational example as a practical validation of our theoretical findings.
Elashiry et al. (Mon,) studied this question.