| 摘要: |
| 本文研究了具有常截曲率c的六维伪黎曼空间型Np6(c)(指标0≤p≤6) 中的λ-双调和超曲面Mr5 (其中r=p-1或p), 证明了当超曲面Mr5的形状算子可对角化时, 其平均曲率必为常数. 应用该结论, 我们证得Np6(c)中的一类双调和超曲面必定是极小的. |
| 关键词: λ-双调和超曲面 伪黎曼空间型 常平均曲率 形状算子 极小 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:Supported by National Natural Science Foundation of China (12161078),Foundation for Innovative Fundamental Research Group Project of Gansu Province (24JRRA778) and Projectof Northwest Normal University (20240010). |
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| λ-BIHARMONIC HYPERSURFACES IN 6-DIMENSIONAL PSEUDO-RIEMANNIAN SPACE FORMS |
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DUAN Zhen-ping, YANG Chao, LIU Jian-cheng, CHEN Jia-rui
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College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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| Abstract: |
| In this paper, we study λ-biharmonic hypersurfaces Mr5 of 6-dimensional pseudoRiemannian space form Np6(c) with the indexs 0 ≤ p ≤ 6, r = p-1 or p, and constant curvature c. It was proved that if the shape operator of Mr5 is diagonalizable, then the mean curvature is a constant. As an application, we find some types of biharmonic hypersurfaces of Np6(c) are minimal. |
| Key words: λ-biharmonic hypersurface pseudo-Riemannian space form constant mean curvature shape operator minimal |
