Combining Principal Normal Indicatrix Curves and Direction Curves with an Alternative Frame
Chapter from the book: Akpınar, A. (ed.) 2023. Research on Mathematics and Science- III.

İlkay Arslan Güven
Gaziantep University
Fatma Çolak
Gaziantep University

Synopsis

This work examined the direction curves of principal normal indicatrix curves regarding a regular curve in Euclidean space of three dimension. The {N,C,W} frame was assigned as a new alternative frame for the mentioned curve. Investigating relationships among the main curve and direction curves using such novel alternative frame is an innovative approach. The Frenet members, curvature, torsion, harmonic curvature and geodesic curvature of direction curves were determined. Direction curve characterizations in the forms of the C-slant helix , slant helix and general helix were provided. In the end, the relevant figures for these curves were displayed.

How to cite this book

Arslan Güven, İ. & Çolak, F. (2023). Combining Principal Normal Indicatrix Curves and Direction Curves with an Alternative Frame. In: Akpınar, A. (ed.), Research on Mathematics and Science- III. Özgür Publications. DOI: https://doi.org/10.58830/ozgur.pub252.c1285

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Published

October 21, 2023

DOI