Simultaneous characterizations of alternative partner-ruled surfaces

In this study, we present partner-ruled surfaces generated by the vectors of the alternative frame of a space curve in Euclidean 3-space. First, each pair of the alternative partner-ruled surfaces to be simultaneously developable and minimal is investigated based on the alternative frame by partial differential equations. Then, simultaneous characterizations of the coordinate curves of these surfaces to be asymptotic, geodesic, and lines of curvature are obtained and explicated. Finally, to illustrate the concepts, the study concludes with an example of alternative partner-ruled surfaces, featuring graphical representations.