On the singularity and distribution parameters of involutive and Bertrandian Frenet ruled surfaces in $\mathbb{E}^{3}$

Abstract

Abstract:In this paper we consider twelve special ruled surfaces associated to the curve α,the involute curve α * and Bertrand mate α * * , with k 1 = 0. They are called as Frenet ruled, involutive Frenet ruled and Bertrandian Frenet ruled surfaces, cause of their generators are the Frenet vector fields of curve α. First we give all the parametrizations of all Frenet ruled surfaces in terms of the Frenet apparatus of curve α. We examined distribution parameters and Singularity of involutive and Bertrand Frenet ruled surfaces based on the Frenet apparatus of curve α in E 3 .