de Sitter空间中全脐超曲面与高斯映照像  

On Totally Umbilical Hypersurfaces of the de Sitter Space and the Gauss Image

作　　者：文海燕 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《西南师范大学学报（自然科学版）》2017年第10期22-25,共4页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：研究de Sitter空间Sn+11中的紧致类空超曲面Mn.利用Minkowski型积分公式,证明了如果存在某个整数r(1≤r≤n-1),使得高阶平均曲率Hr在Mn上是非零常数,且Mn的高斯映照像包含在一个开半球面内,则超曲面Mn全脐.The totally umbilical property of compact space-like hypersurface Mnin de Sitter space has been studied.By using a known Minkowski integral formula,under the condition that there exists an integer r（1≤r≤n-1）such that the higher order mean curvature Hris nonzero constant everywhere,it is proved that Mnis totally umbilical if the Gauss image of Mnis contained in an open hemisphere.

关 键 词：DE SITTER空间 全脐超曲面 高斯映照像 高阶平均曲率 

分 类 号：O186.12[理学—数学]