Simultaneous Developability of Partner Ruled Surfaces according to Darboux Frame in E3

Abstract

In this paper, we introduce original definitions of Partner ruled surfaces according to the Darboux frame of a curve lying on an arbitrary regular surface in $E^3$. It concerns $Tg$ Partner ruled surfaces, $Tn$ Partner ruled surfaces, and $gn$ Partner ruled surfaces. We aim to study the simultaneous developability conditions of each couple of two Partner ruled surfaces. Finally, we give an illustrative example for our study.