Superconformal ruled surfaces in $mathbb{E}^{4}$

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 $mathbb{E}^{4}.$ 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 $mathbb{E}^{4}$ to become superconformal. We also show that superconformal ruled surfaces in $mathbb{E}^{4}$ are Chen surfaces