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Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures
Journal of Function Spaces ( IF 1.9 ) Pub Date : 2020-08-01 , DOI: 10.1155/2020/2182975
Chao Yang 1 , Jiancheng Liu 1
Affiliation  

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form with constant sectional curvature and index have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces in even-dimensional pseudo-Euclidean space , in even-dimensional de Sitter space , and in even-dimensional anti-de Sitter space are minimal.

中文翻译:

具有最多两个不同主曲率的伪-Riemann空间形式的双调超曲面

在本文中,我们证明在伪黎曼空间形式中具有最多两个截然不同的主曲率且截面曲率和折射率恒定的双调和超曲面具有恒定的平均曲率。此外,我们发现在偶数维德西特空间偶数维德西特空间中的此类双调和超曲面 并且在反维Sitter空间中 是最小的。
更新日期:2020-08-01
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