Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3

Abstract

In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in $E^3$. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.