| 赵艳,刘西民.一类浸入在半黎曼卷积空间的完备超曲面[J].数学研究及应用,2016,36(6):723~731 |
| 一类浸入在半黎曼卷积空间的完备超曲面 |
| A Class of Complete Hypersurfaces Immersed in Semi-Riemannian Warped Product Spaces |
| 投稿时间：2015-10-19 修订日期：2016-03-09 |
| DOI：10.3770/j.issn:2095-2651.2016.06.012 |
| 中文关键词: 半黎曼流形 卷积 完备超曲面 高度函数 |
| 英文关键词:semi-Riemannian manifold warped product complete hypersurface height function |
| 基金项目:国家自然科学基金(Nos.11371076; 11431009). |
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| 摘要点击次数: 2102 |
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| 中文摘要: |
| 我们研究的是浸入在半黎曼卷积空间$\epsilon\textit{I}\times _{f}M^{n}$的完备超曲面,其中$M^{n}$是连通的$n$维可定向黎曼流形.当纤维$M^{n}$是完备的,并且界面曲率$-k\leq K_{M}$, 其中$k$为正常数,对于高度函数$h$,如果对其梯度的范数进行适当限制,我们得到浸入在半黎曼卷积空间的完备超曲面是切片.我们运用的原理是是著名的推广的极大值原理. |
| 英文摘要: |
| We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type $\epsilon\textit{I}\times _{f}M^{n}$, where $M^{n}$ is a connected $n$-dimensional oriented Riemannian manifold. When the fiber $M^{n}$ is complete with sectional curvature $-k\leq K_{M}$ for some positive constant $k$, under appropriate restrictions on the norm of the gradient of the height function $h$, we proceed with our technique in order to guarantee that complete hypersurface immersed in a semi-Riemannian warped product is a slice. Our approach is based on the well known generalized maximum principle and another suitable maximum principle at the infinity due to Yau. |
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