关于欧氏空间中超球面的特征

Characterization of the Hypersphere in Euclidean Space

本文在S.S.Chern^(1989)得到了欧氏空间中超球面的一个特征的基础上,获得了另一种特征,从而推广了他的结果.

In this paper,the following result is shown:Let ∑ be a closed strictly convexhypersurface in euclidean space E^(n+1)(n≥2)with(?)=const.,where 1≤l(1)<l(2)<…<l(p)≤n,α(i)/α(p)≥0,i=2,3,…,p-1,(p≤n),(α(1)l(1)++α(2)l(2)+…+α(P)l(p))/α(p)l(p)>0,Then ∑ is a hypersphere.