一类对称多项式在微分几何中的应用

A CLASS OF SYMMETRIC POLYNOMIAL AND ITS APPLICATIONS ON DIFFERENTIAL GEOMETRY

本文研究了卵形面特征刻画.利用麦克劳林不等式及对称多项式的性质,获得了一个An+1中的卵形面,若其任意三个连续高阶仿射平均曲率乘积为常熟,且Ln=0,则该卵形面为椭圆的结果.推广了现有文献关于卵形面的刻画结果.

In this paper,we study the charachters of ovaloid.By using the Machaurin＇s inequality and symmetric polynomial,we prove that an ovaloid in An＋1is an ellipsoid if the product of its three random continuous affine mean cervatures is constant and Ln = 0,which is a generalization of the characterization of ovaloid.