A Class of Complete Hypersurfaces Immersed in Semi-Riemannian Warped Product Spaces

DOI：10.3770/j.issn:2095-2651.2016.06.012

 作者 单位 赵艳 大连理工大学数学科学学院, 辽宁 大连 116024 刘西民 大连理工大学数学科学学院, 辽宁 大连 116024

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.

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.