On simultaneous characterizations of partner-ruled surfaces with Sasai’s interpretation

In this study, the partner-ruled surfaces in Euclidean 3-space are introduced based on the vector fields of a space curve associated with the element of a modified orthogonal frame incorporating curvatures. First, the necessary conditions for each pair of partner-ruled surfaces to be simultaneously developable and minimal are investigated. Furthermore, simultaneous characterizations are provided for the parameter curves of these surfaces to be asymptotic curves, lines of curvature, and geodesics. Finally, to illustrate the theoretical results, an example of partner-ruled surfaces is presented along with their graphical representations.