| 摘要: |
| 本文研究了具有常截曲率 c 的六维伪黎曼空间型 N^6_p(c) (指标 0≤ p≤ 6) 中的 λ-双调和超曲面 M^5_r (其中 r=p-1 或 p), 证明了当超曲面 M^5_r 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 N^6_p(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:国家自然科学基金(地区项目） |
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| λ-BIHARMONIC HYPERSURFACES IN 6-DIMENSIONAL PSEUDO-RIEMANNIAN SPACE FORMS |
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Duan Zhenping, Yang Chao
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Northwest Normal University
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| Abstract: |
| In this paper, we study λ-biharmonic hypersurfaces M^5_r of 6-dimensional pseudo-Riemannian space form N^6_p(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 M^5_r is diagonalizable, then the mean curvature is a constant. As an application, we find some types of biharmonic hypersurfaces of N^6_p(c) are minimal. |
| Key words: λ-biharmonic hypersurface pseudo-Riemannian space form constant mean curvature shape operator minimal. |
