摘要
针对(n+1)维欧氏空间Rn+1中紧致无边凸超曲面M,利用一个已知的积分公式,并提出一种新的技巧,证明了:如果存在一个整数r(1≤r≤n-1)使得M的第r阶高阶平均曲率Hr是常数,并且M的高斯映照是到标准单位球面Sn的拓扑同胚,则M全脐.
For an oriented,compact and convex hypersurface M without boundary in the( n + 1)-dimensional Euclidean space Rn+1,we apply a known integral formula and put out a new skill to prove that if there exits an integer r( 1≤r≤n-1) such that the r-mean curvature Hris a constant and if the Gauss map of M is a topological homeomorphism onto the standard unit sphere Sn,then M is totally umbilical.
作者
王琪
WANG Qi(School of Mathematics and Information Science,Guiyang University,Guiyang,Guizhou 550005, Chin)
出处
《福州大学学报(自然科学版)》
CAS
北大核心
2018年第3期307-310,共4页
Journal of Fuzhou University(Natural Science Edition)
基金
贵州省科学技术基金资助项目(黔科合LH字[2015]7298)
关键词
欧氏空间
凸超曲面
高阶平均曲率
高斯映照
全脐性质
Euclidean space
convex hypersurface
higher order mean curvature
Gauss map
totally umbilical property