| 摘要: |
| 本文研究了单位球中的数量曲率满足r=aH+b的完备超曲面的问题.利用极值原理的方法,获得了超曲面的一个刚性结果,推广了这一类具有常中曲率或者常数量曲率超曲面的结果. |
| 关键词: 单位球 数量曲率 全脐超曲面 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:国家自然基金资助(61271002) |
|
| RIGIDITY THEOREM FOR COMPLETE HYPERSURFACES IN UNIT SPHERE |
|
ZHANG Shi-cheng
|
|
School of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China
|
| Abstract: |
| In this paper,the complete hypersurfaces with scalar curvature r satisfying r=aH+b is discussed in unit sphere Sn+1(1),the maximum principle can be applied and a rigidity theorem is obtained for these hypersurfaces.The result is the generalization of several results for the hypersurface with constant mean curvature or constant scalar curvature. |
| Key words: unit sphere scalar curvature totally umbilical hypersurfac |
