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一类浸入在半黎曼卷积空间的完备超曲面
引用本文: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
作者姓名:赵艳  刘西民
作者单位:大连理工大学数学科学学院, 辽宁 大连 116024,大连理工大学数学科学学院, 辽宁 大连 116024
基金项目:国家自然科学基金(Nos.11371076; 11431009).
摘    要:We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type eI×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≤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.

关 键 词:半黎曼流形   卷积   完备超曲面   高度函数
收稿时间:2015-10-19
修稿时间:2016-03-09

A Class of Complete Hypersurfaces Immersed in Semi-Riemannian Warped Product Spaces
Yan ZHAO and Ximin LIU. A Class of Complete Hypersurfaces Immersed in Semi-Riemannian Warped Product Spaces[J]. Journal of Mathematical Research with Applications, 2016, 36(6): 723-731
Authors:Yan ZHAO and Ximin LIU
Affiliation:School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China and School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
Abstract:We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type $epsilontextit{I}times _{f}M^{n}$, where $M^{n}$ is a connected $n$-dimensional oriented Riemannian manifold. When the fiber $M^{n}$ is complete with sectional curvature $-kleq K_{M}$ 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.
Keywords:semi-Riemannian manifold   warped product   complete hypersurface   height function
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