Superconformal ruled surfaces in E4

Abstract

In the present study we consider ruled surfaces imbedded in a Euclidean space of four dimensions. We also give some special examples of ruled surfaces in E-4. Further, the curvature properties of these surface are investigated with respect to variation of normal vectors and curvature ellipse. Finally, we give a necessary and sufficient condition for ruled surfaces in E-4 to become superconformal. We also show that superconformal ruled surfaces in E-4 are Chen surfaces.