(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This paper introduces three distinct types of ruled surfaces, namely, the quasi-tangent surfaces , the quasi-normal surfaces, and the quasi-binormal surfaces. These types are determined by the orientation of their direction curves tangent, normal, and binormal to the base curve, respectively. This paper does not only introduce these surfaces but also determine their fundamental properties, including the first, the second, and the third fundamental forms, as well as the Gaussian and the mean curvatures. Also, the geodesic curvature, the normal curvature, and the geodesic torsion associated with the base curve for each type of surface are investigated. Furthermore, the conditions for the base curve to be as a geodesic, an asymptotic line, and a principal line for each type of surface are provided. Also, the conditions for these curves to be considered developable and minimal surfaces are introduced. Moreover, two illustrative examples are introduced to obtain our results