Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$

In this present paper, rectifying curves are re-characterized in a shorter and simpler way using harmonic curvatures and some relations between rectifying curves and focal curves are found in terms of their harmonic curvature functions in $n-$dimensional Euclidean space. Then, a rectifying Salkowski...

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Main Authors: Yusuf Yaylı, Beyhan Yılmaz, İsmail Gök
Format: Article
Language:English
Published: Mahmut Akyigit 2022-04-01
Series:Journal of Mathematical Sciences and Modelling
Subjects:
Online Access:https://dergipark.org.tr/tr/download/article-file/2019630
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author Yusuf Yaylı
Beyhan Yılmaz
İsmail Gök
author_facet Yusuf Yaylı
Beyhan Yılmaz
İsmail Gök
author_sort Yusuf Yaylı
collection DOAJ
description In this present paper, rectifying curves are re-characterized in a shorter and simpler way using harmonic curvatures and some relations between rectifying curves and focal curves are found in terms of their harmonic curvature functions in $n-$dimensional Euclidean space. Then, a rectifying Salkowski curve, which is the focal curve of a given space curve is investigated. Finally, some figures related to the theory are given in the case $n=3$.
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spelling doaj.art-1eedee6a5e8646a281f8c2b398f2e3a42024-01-18T06:28:16ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922022-04-015181510.33187/jmsm.10078571408Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$Yusuf Yaylı0Beyhan Yılmaz1İsmail Gök2ANKARA UNIVERSITYKAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİANKARA UNIVERSITYIn this present paper, rectifying curves are re-characterized in a shorter and simpler way using harmonic curvatures and some relations between rectifying curves and focal curves are found in terms of their harmonic curvature functions in $n-$dimensional Euclidean space. Then, a rectifying Salkowski curve, which is the focal curve of a given space curve is investigated. Finally, some figures related to the theory are given in the case $n=3$.https://dergipark.org.tr/tr/download/article-file/2019630focal curveharmonic curvaturerectifying curve.
spellingShingle Yusuf Yaylı
Beyhan Yılmaz
İsmail Gök
Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$
Journal of Mathematical Sciences and Modelling
focal curve
harmonic curvature
rectifying curve.
title Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$
title_full Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$
title_fullStr Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$
title_full_unstemmed Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$
title_short Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$
title_sort differential equations of rectifying curves and focal curves in mathbb e n
topic focal curve
harmonic curvature
rectifying curve.
url https://dergipark.org.tr/tr/download/article-file/2019630
work_keys_str_mv AT yusufyaylı differentialequationsofrectifyingcurvesandfocalcurvesinmathbben
AT beyhanyılmaz differentialequationsofrectifyingcurvesandfocalcurvesinmathbben
AT ismailgok differentialequationsofrectifyingcurvesandfocalcurvesinmathbben