Hypersurfaces satisfying $\triangle \vec {H}=\lambda \vec {H}$ in $\mathbb{E}_{\lowercase{s}}^{5}$
| Autor: | Gupta, Ram Shankar, Arvanitoyeorgos, Andreas |
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| Rok vydání: | 2024 |
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| Zdroj: | J. Math. Anal. Appl. 525(2) (2023) Article 127182 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2023.127182 |
| Popis: | In this paper, we study hypersurfaces $M_{r}^{4}$ $(r=0, 1, 2, 3, 4)$ satisfying $\triangle \vec{H}=\lambda \vec{H}$ ($\lambda$ a constant) in the pseudo-Euclidean space $\mathbb{E}_{s}^{5}$ $(s=0, 1, 2, 3, 4, 5)$. We obtain that every such hypersurface in $\mathbb{E}_{s}^{5}$ with diagonal shape operator has constant mean curvature, constant norm of second fundamental form and constant scalar curvature. Also, we prove that every biharmonic hypersurface in $\mathbb{E}_{s}^{5}$ with diagonal shape operator must be minimal. Comment: 19 pages |
| Databáze: | arXiv |
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