Some integral curves with a new frame
In this paper, some new integral curves are defined in three-dimensional Euclidean space by using a new frame of a polynomial spatial curve. The Frenet vectors, curvature and torsion of these curves are obtained by means of new frame and curvatures. We give the characterizations and properties of th...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-11-01
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| Series: | Open Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0078/math-2020-0078.xml?format=INT |
| _version_ | 1818339292515139584 |
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| author | Güven İlkay Arslan |
| author_facet | Güven İlkay Arslan |
| author_sort | Güven İlkay Arslan |
| collection | DOAJ |
| description | In this paper, some new integral curves are defined in three-dimensional Euclidean space by using a new frame of a polynomial spatial curve. The Frenet vectors, curvature and torsion of these curves are obtained by means of new frame and curvatures. We give the characterizations and properties of these integral curves under which conditions they are general helix. Also, the relationships between these curves in terms of being some kinds of associated curves are introduced. Finally, an example is illustrated. |
| first_indexed | 2024-12-13T15:24:41Z |
| format | Article |
| id | doaj.art-bf5907071c974f668cb2e8f6eb3d4805 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-13T15:24:41Z |
| publishDate | 2020-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-bf5907071c974f668cb2e8f6eb3d48052022-12-21T23:40:25ZengDe GruyterOpen Mathematics2391-54552020-11-011811332134110.1515/math-2020-0078math-2020-0078Some integral curves with a new frameGüven İlkay Arslan0Faculty of Arts and Science, Department of Mathematics, Gaziantep University, Gaziantep, TurkeyIn this paper, some new integral curves are defined in three-dimensional Euclidean space by using a new frame of a polynomial spatial curve. The Frenet vectors, curvature and torsion of these curves are obtained by means of new frame and curvatures. We give the characterizations and properties of these integral curves under which conditions they are general helix. Also, the relationships between these curves in terms of being some kinds of associated curves are introduced. Finally, an example is illustrated.http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0078/math-2020-0078.xml?format=INTgeneral helixassociated curveintegral curveflc-frame53a0414h50 |
| spellingShingle | Güven İlkay Arslan Some integral curves with a new frame Open Mathematics general helix associated curve integral curve flc-frame 53a04 14h50 |
| title | Some integral curves with a new frame |
| title_full | Some integral curves with a new frame |
| title_fullStr | Some integral curves with a new frame |
| title_full_unstemmed | Some integral curves with a new frame |
| title_short | Some integral curves with a new frame |
| title_sort | some integral curves with a new frame |
| topic | general helix associated curve integral curve flc-frame 53a04 14h50 |
| url | http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0078/math-2020-0078.xml?format=INT |
| work_keys_str_mv | AT guvenilkayarslan someintegralcurveswithanewframe |