Characterizations of Euclidean spheres
We use the tangential component $ \psi ^{T} $ of an immersion of a compact hypersurface of the Euclidean space $ \mathbf{E}^{m+1} $ in finding two characterizations of a sphere. In first characterization, we use $ \psi ^{T} $ as a geodesic vector field (vector field with all its trajectories geodesi...
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AIMS Press
2021-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021449?viewType=HTML |
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doaj-df6a38cf86cf431c8787d8e1d1fd4f222021-05-26T02:11:28ZengAIMS PressAIMS Mathematics2473-69882021-05-01677733774010.3934/math.2021449Characterizations of Euclidean spheresSharief Deshmukh0Mohammed Guediri1Department of Mathematics, College of Science, King Saud University, P. O. Box-2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P. O. Box-2455, Riyadh 11451, Saudi ArabiaWe use the tangential component $ \psi ^{T} $ of an immersion of a compact hypersurface of the Euclidean space $ \mathbf{E}^{m+1} $ in finding two characterizations of a sphere. In first characterization, we use $ \psi ^{T} $ as a geodesic vector field (vector field with all its trajectories geodesics) and in the second characterization, we use $ \psi ^{T} $ to annihilate the de-Rham Laplace operator on the hypersurface. https://www.aimspress.com/article/doi/10.3934/math.2021449?viewType=HTMLgeodesic vector fieldde-rham laplace operatorsupport functioneuclidean spacesphere |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sharief Deshmukh Mohammed Guediri |
| spellingShingle |
Sharief Deshmukh Mohammed Guediri Characterizations of Euclidean spheres AIMS Mathematics geodesic vector field de-rham laplace operator support function euclidean space sphere |
| author_facet |
Sharief Deshmukh Mohammed Guediri |
| author_sort |
Sharief Deshmukh |
| title |
Characterizations of Euclidean spheres |
| title_short |
Characterizations of Euclidean spheres |
| title_full |
Characterizations of Euclidean spheres |
| title_fullStr |
Characterizations of Euclidean spheres |
| title_full_unstemmed |
Characterizations of Euclidean spheres |
| title_sort |
characterizations of euclidean spheres |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2021-05-01 |
| description |
We use the tangential component $ \psi ^{T} $ of an immersion of a compact hypersurface of the Euclidean space $ \mathbf{E}^{m+1} $ in finding two characterizations of a sphere. In first characterization, we use $ \psi ^{T} $ as a geodesic vector field (vector field with all its trajectories geodesics) and in the second characterization, we use $ \psi ^{T} $ to annihilate the de-Rham Laplace operator on the hypersurface. |
| topic |
geodesic vector field de-rham laplace operator support function euclidean space sphere |
| url |
https://www.aimspress.com/article/doi/10.3934/math.2021449?viewType=HTML |
| work_keys_str_mv |
AT shariefdeshmukh characterizationsofeuclideanspheres AT mohammedguediri characterizationsofeuclideanspheres |
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