Research Communication | Open Access
Volume 2020 | Communication ID 172 |

Some associated curves of normal indicatrix of a regular curve

Nidal Echabbi, Amina Ouazzani Chahdi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
30 January 2020
14 February 2020
10 March 2020

Abstract: In this paper, we consider integral curves of a vector field generated by Frenet vectors of normal indicatrix of a given curve in Euclidean 3-space. We define some new associated curves such as evolute direction curves, Bertrand direction curves and Mannheim directon curves of the normal indicatrix of a regular curve, respectively. We also found the relationships between curvatures of these curves. By using these associated curves, we give a new approach to construct slant helices and C- slant helices. Finally, we present some examples.