Abstract

We analyzed the problem of finding a surfaces family through a null curve with Cartan frame. We constructed a differential equation system such that a given null curve is an isogeodesic curve on a surface. In addition, developablity along the common null geodesic of the members of surface family are discussed. The extension to ruled surfaces is also outlined. Finally, we demonstrated some interesting surfaces about subject.

Key words: Cartan frame; surface family; common geodesic; ruled surface.