Surfaces of coordinate finite $ II $-type
We study the class of surfaces of revolution in the 3-dimensional Euclidean space $ E^{3} $ with nonvanishing Gauss curvature whose position vector $ \boldsymbol{x} $ satisfies the condition $ \Delta^{II}\boldsymbol{x} = A\boldsymbol{x} $, where $ A $ is a square matrix of order 3 and $ \Delta^{II}...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025285 |
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| author | Mutaz Al-Sabbagh |
| author_facet | Mutaz Al-Sabbagh |
| author_sort | Mutaz Al-Sabbagh |
| collection | DOAJ |
| description | We study the class of surfaces of revolution in the 3-dimensional Euclidean space $ E^{3} $ with nonvanishing Gauss curvature whose position vector $ \boldsymbol{x} $ satisfies the condition $ \Delta^{II}\boldsymbol{x} = A\boldsymbol{x} $, where $ A $ is a square matrix of order 3 and $ \Delta^{II} $ denotes the Laplace operator of the second fundamental form $ II $ of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere. |
| format | Article |
| id | doaj-art-7d7ee93a1f674008b8398b885bdac5e4 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-7d7ee93a1f674008b8398b885bdac5e42025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-03-011036258626910.3934/math.2025285Surfaces of coordinate finite $ II $-typeMutaz Al-Sabbagh0Department of Basic Engineering Sciences, Imam Abdulrahman bin Faisal University, Dammam 31441, Saudi ArabiaWe study the class of surfaces of revolution in the 3-dimensional Euclidean space $ E^{3} $ with nonvanishing Gauss curvature whose position vector $ \boldsymbol{x} $ satisfies the condition $ \Delta^{II}\boldsymbol{x} = A\boldsymbol{x} $, where $ A $ is a square matrix of order 3 and $ \Delta^{II} $ denotes the Laplace operator of the second fundamental form $ II $ of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.https://www.aimspress.com/article/doi/10.3934/math.2025285surfaces in $ e^{3} $surfaces of revolutionsurfaces of coordinate finite typebeltrami operator |
| spellingShingle | Mutaz Al-Sabbagh Surfaces of coordinate finite $ II $-type AIMS Mathematics surfaces in $ e^{3} $ surfaces of revolution surfaces of coordinate finite type beltrami operator |
| title | Surfaces of coordinate finite $ II $-type |
| title_full | Surfaces of coordinate finite $ II $-type |
| title_fullStr | Surfaces of coordinate finite $ II $-type |
| title_full_unstemmed | Surfaces of coordinate finite $ II $-type |
| title_short | Surfaces of coordinate finite $ II $-type |
| title_sort | surfaces of coordinate finite ii type |
| topic | surfaces in $ e^{3} $ surfaces of revolution surfaces of coordinate finite type beltrami operator |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025285 |
| work_keys_str_mv | AT mutazalsabbagh surfacesofcoordinatefiniteiitype |