On Classes of Surfaces with a Common Special Curve - Etemad Dehkordy, Azam (Jordan Journal of Mathematics and Statistics, 2025)
In recent years, many researchers have studied surfaces with common geodesic or common line of curvature in different spaces. In this paper we give necessary and sufficient conditions for some classes of surfaces in the three dimensional Euclidean space E^3 to have a curve as common geodesic or common line of curvature. Precisely, for a given curve, we suggest a family of surfaces which have it as their common line of curvature or common geodesic. Moreover, we illustrate the results by examples.