关于n维单形的一个不等式

设∑_A 是 E~n 中的 n 维单形:e_1,e_2…e_(n+1)分别是∑_A 的 n+1个界面上的单位法向量,令Di=det(e_1,e_2,…ei-1,e_(i+1)…e_(n+1)),a_1=arcsin|D|,本文获得了下列不等式sum from i=1 to n+1 λ_1sin~2a_1≤(λ1(1/n sum from i=1 to n+1 1/λ_1)~n这里λ_1∈R~+,i=1,2,…n+1

About an Inequality of N-Dimensional Single Form

Suppose ∑A is n—dimensional single form in E~: ej_1,e_2,…e_(n+1) are respectivly unit vectors on n+1 interfaces of ∑A。Let D_i=det (e_1,e_2,… e_(i-1)·e_ie_(i+1),…e_(n+1)α_i=arc sin |D_i| The following inequality is obtained from this article: sum from i=1 to n+1 λ_isin~2α≤(λ_i)(1/n (sum from i=1 to n+1) 1/λ_i)~n Here,λ_i∈R~(-1),i=1,2,…n+1。