Evolution of space curves and the special ruled surfaces with modified orthogonal frame
In this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-02-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020134/fulltext.html |
| _version_ | 1828346275500654592 |
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| author | Kemal Eren Hidayet Huda Kosal |
| author_facet | Kemal Eren Hidayet Huda Kosal |
| author_sort | Kemal Eren |
| collection | DOAJ |
| description | In this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations. Moreover, we determine the first and second fundamental forms, the Gaussian and mean curvatures of the tangent, normal, and binormal ruled surfaces according to the modified frame. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces based on modified orthogonal frame. |
| first_indexed | 2024-04-14T00:24:10Z |
| format | Article |
| id | doaj.art-ee0071df69ca4cd3b27168d22dc4dbc2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-14T00:24:10Z |
| publishDate | 2020-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ee0071df69ca4cd3b27168d22dc4dbc22022-12-22T02:22:50ZengAIMS PressAIMS Mathematics2473-69882020-02-01532027203910.3934/math.2020134Evolution of space curves and the special ruled surfaces with modified orthogonal frameKemal Eren0Hidayet Huda Kosal1Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, 54187 TurkeyDepartment of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, 54187 TurkeyIn this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations. Moreover, we determine the first and second fundamental forms, the Gaussian and mean curvatures of the tangent, normal, and binormal ruled surfaces according to the modified frame. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces based on modified orthogonal frame.https://www.aimspress.com/article/10.3934/math.2020134/fulltext.htmlmodified orthogonal frameevolution of curvesmoke ring equationsruled surfacesgaussian curvaturemean curvature |
| spellingShingle | Kemal Eren Hidayet Huda Kosal Evolution of space curves and the special ruled surfaces with modified orthogonal frame AIMS Mathematics modified orthogonal frame evolution of curve smoke ring equations ruled surfaces gaussian curvature mean curvature |
| title | Evolution of space curves and the special ruled surfaces with modified orthogonal frame |
| title_full | Evolution of space curves and the special ruled surfaces with modified orthogonal frame |
| title_fullStr | Evolution of space curves and the special ruled surfaces with modified orthogonal frame |
| title_full_unstemmed | Evolution of space curves and the special ruled surfaces with modified orthogonal frame |
| title_short | Evolution of space curves and the special ruled surfaces with modified orthogonal frame |
| title_sort | evolution of space curves and the special ruled surfaces with modified orthogonal frame |
| topic | modified orthogonal frame evolution of curve smoke ring equations ruled surfaces gaussian curvature mean curvature |
| url | https://www.aimspress.com/article/10.3934/math.2020134/fulltext.html |
| work_keys_str_mv | AT kemaleren evolutionofspacecurvesandthespecialruledsurfaceswithmodifiedorthogonalframe AT hidayethudakosal evolutionofspacecurvesandthespecialruledsurfaceswithmodifiedorthogonalframe |