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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Format: | Article |
Language: | English |
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Mahmut Akyigit
2022-04-01
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Series: | Journal of Mathematical Sciences and Modelling |
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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 $n=3$. |
first_indexed | 2024-03-08T13:16:02Z |
format | Article |
id | doaj.art-1eedee6a5e8646a281f8c2b398f2e3a4 |
institution | Directory Open Access Journal |
issn | 2636-8692 |
language | English |
last_indexed | 2024-03-08T13:16:02Z |
publishDate | 2022-04-01 |
publisher | Mahmut Akyigit |
record_format | Article |
series | Journal of Mathematical Sciences and Modelling |
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 |
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