Framed Natural Mates of Framed Curves in Euclidean 3-Space
In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a fra...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3571 |
| _version_ | 1827729282523201536 |
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| author | Yanlin Li Mahmut Mak |
| author_facet | Yanlin Li Mahmut Mak |
| author_sort | Yanlin Li |
| collection | DOAJ |
| description | In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples. |
| first_indexed | 2024-03-10T23:45:46Z |
| format | Article |
| id | doaj.art-92c7ddd536dc4889ace0ff94dd887e0d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:46Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-92c7ddd536dc4889ace0ff94dd887e0d2023-11-19T02:03:58ZengMDPI AGMathematics2227-73902023-08-011116357110.3390/math11163571Framed Natural Mates of Framed Curves in Euclidean 3-SpaceYanlin Li0Mahmut Mak1School of Mathematics, Hangzhou Normal University, Hangzhou 311121, ChinaDepartment of Mathematics, Kırşehir Ahi Evran University, Kırşehir 40100, TurkeyIn this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples.https://www.mdpi.com/2227-7390/11/16/3571framed curvespherical curvehelixslant helixrectifying curve |
| spellingShingle | Yanlin Li Mahmut Mak Framed Natural Mates of Framed Curves in Euclidean 3-Space Mathematics framed curve spherical curve helix slant helix rectifying curve |
| title | Framed Natural Mates of Framed Curves in Euclidean 3-Space |
| title_full | Framed Natural Mates of Framed Curves in Euclidean 3-Space |
| title_fullStr | Framed Natural Mates of Framed Curves in Euclidean 3-Space |
| title_full_unstemmed | Framed Natural Mates of Framed Curves in Euclidean 3-Space |
| title_short | Framed Natural Mates of Framed Curves in Euclidean 3-Space |
| title_sort | framed natural mates of framed curves in euclidean 3 space |
| topic | framed curve spherical curve helix slant helix rectifying curve |
| url | https://www.mdpi.com/2227-7390/11/16/3571 |
| work_keys_str_mv | AT yanlinli framednaturalmatesofframedcurvesineuclidean3space AT mahmutmak framednaturalmatesofframedcurvesineuclidean3space |