On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion
If both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and surface flows. In this paper, we study inexte...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023573?viewType=HTML |
| _version_ | 1797861300060028928 |
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| author | Nural Yüksel Burçin Saltık |
| author_facet | Nural Yüksel Burçin Saltık |
| author_sort | Nural Yüksel |
| collection | DOAJ |
| description | If both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and surface flows. In this paper, we study inextensible tangential, normal and binormal ruled surfaces generated by a curve with constant torsion, which is also called a Salkowski curve. We investigate whether or not these surfaces are minimal or can be developed. In addition, we prove some theorems which are related to inextensible ruled surfaces within three-dimensional Euclidean space. |
| first_indexed | 2024-04-09T22:00:00Z |
| format | Article |
| id | doaj.art-a896119a5f7e4abe91af717abd51f813 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T22:00:00Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a896119a5f7e4abe91af717abd51f8132023-03-24T01:25:15ZengAIMS PressAIMS Mathematics2473-69882023-03-0185113121132410.3934/math.2023573On inextensible ruled surfaces generated via a curve derived from a curve with constant torsionNural Yüksel0Burçin Saltık1Department of Mathematics, Erciyes University, 38039 Kayseri, TurkeyDepartment of Mathematics, Erciyes University, 38039 Kayseri, TurkeyIf both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and surface flows. In this paper, we study inextensible tangential, normal and binormal ruled surfaces generated by a curve with constant torsion, which is also called a Salkowski curve. We investigate whether or not these surfaces are minimal or can be developed. In addition, we prove some theorems which are related to inextensible ruled surfaces within three-dimensional Euclidean space.https://www.aimspress.com/article/doi/10.3934/math.2023573?viewType=HTMLruled surfacegaussian curvaturemean curvatureinextensible surfaceconstant curvature |
| spellingShingle | Nural Yüksel Burçin Saltık On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion AIMS Mathematics ruled surface gaussian curvature mean curvature inextensible surface constant curvature |
| title | On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion |
| title_full | On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion |
| title_fullStr | On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion |
| title_full_unstemmed | On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion |
| title_short | On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion |
| title_sort | on inextensible ruled surfaces generated via a curve derived from a curve with constant torsion |
| topic | ruled surface gaussian curvature mean curvature inextensible surface constant curvature |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023573?viewType=HTML |
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