福州大学学报（自然科学版）2018，Vol.46Issue(3)：307-310,4.DOI:10.7631/issn.1000-2243.17047
欧氏空间中常高阶平均曲率紧致凸超曲面与高斯映像
On the Gauss image of compact and convex hypersurfaces with a constant higher order mean curvature in Euclidean space
摘要
Abstract
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 Hr is a constant and if the Gauss map of M is a topological homeomorphism onto the standard unit sphere Sn, then M is totally umbilical.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Key words
Euclidean space/convex hypersurface/higher order mean curvature/Gauss map/totally umbilical property分类
数理科学引用本文复制引用
王琪..欧氏空间中常高阶平均曲率紧致凸超曲面与高斯映像[J].福州大学学报（自然科学版）,2018,46(3):307-310,4.基金项目
贵州省科学技术基金资助项目(黔科合LH字[2015]7298) （黔科合LH字[2015]7298）
