Revisiting surfaces with a common null geodesic curve in Minkowski 3-space 𝔼13

Abstract

In this paper, we study the problem of constructing a surface family from a given null geodesic curve in Minkowski 3-space [Formula: see text]. Using the Cartan frame of the given null curve, we present the surface tangent plane is coincident with the curve rectifying plane, and analyze the necessary and sufficient condition for that curve to be null geodesic. Then, the extension to ruled, and developable surfaces are also outlined. As an application, we derive an explicit solution of the Da Rios vortex filament equation lying in the B-scroll.