Surfaces of coordinate finite II-type
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929674380115968 |
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| author | Al-Zoubi, Hassan Al-Sabbagh, Mutaz Hamadneh, Tareq |
| author_facet | Al-Zoubi, Hassan Al-Sabbagh, Mutaz Hamadneh, Tareq |
| contents | In this article, 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 $Δ^{II}\boldsymbol{x}=A\boldsymbol{x}$, where $A$ is a square matrix of order 3 and $Δ^{II}$ 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_05120 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Surfaces of coordinate finite II-type Al-Zoubi, Hassan Al-Sabbagh, Mutaz Hamadneh, Tareq General Mathematics In this article, 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 $Δ^{II}\boldsymbol{x}=A\boldsymbol{x}$, where $A$ is a square matrix of order 3 and $Δ^{II}$ 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. |
| title | Surfaces of coordinate finite II-type |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2005.05120 |