Quadric surfaces of coordinate finite type Gauss map
| Autor: | Al-Zoubi, Hassan, Hamadneh, Tareq |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type Gauss map with respect to the second fundamental form $II$, i.e., their Gauss map vector $\boldsymbol{n}$ satisfies the relation $\Delta ^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$, where $\Delta ^{II}$ denotes the Laplace operator of the second fundamental form $II$ of the surface and $\varLambda$ is a square matrix of order 3. We show that helicoids and spheres are the only class of surfaces mentioned above satisfying $\Delta ^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$. Comment: arXiv admin note: text overlap with arXiv:1610.05102 |
| Databáze: | arXiv |
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