Some curve pairs according to types of Bishop frame

Abstract

In the present paper, we investigate the associated curves of the normal indicatrix of a regular curve in Euclidean $ 3- $space. We obtain the versions of the Bishop frame rotating around the Frenet elements of the normal indicatrix. As a result, we show that these associated curves are the elements of the versions of Bishop frame in Euclidean 3-space.

Keywords

• evolute curve
• mannheim curve
• bertrand curve
• normal indicatrix
• versions of bishop frame
• euclidean space