Open AccessSome Associated Curves of Normal Indicatrix of a Regular Curve
Author(s) -
Nidal Echabbi,
Amina Ouazzani Chahdi
Publication year - 2020
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v12n1p84
Subject(s) - frenet–serret formulas , mathematics , euclidean geometry , mathematical analysis , space (punctuation) , vector field , euclidean space , geometry , pure mathematics , curvature , philosophy , linguistics
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.