An examination on the positions of frenet ruled surfaces Along Bertrand Pairs α and α* according to their normal vector fields in E3

Abstract

In this paper we consider eight special Frenet ruled surfaces along to the Bertrand pairs (α*,α). First we define and find the parametric equations of Frenet ruled surfaces which are called Bertrandian Frenet ruled surface, along Bertrand curve α, in terms of the Frenet apparatus of Bertrand curve α. Later we find only one matrix gives us all sixteen positions of normal vector fields of eight Frenet ruled surfaces and Bertrandian Frenet ruled surface in terms of Frenet apparatus of Bertrand curve α too. Further using that matrix we have some results such as; normal ruled surface and Bertrandian tangent ruled surface have perpendicular normal vector fields along the curve V2 or there are four pairs of Frenet ruled surface with perpendicular normal vector fields along the Bertrand pairs (α*,α) . © 2015 Ş. Kiliçoğlu, S. Şenyurt and H. H. Hacisalihoğlu.