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+1 is an ellipsoid if the product of its three random continuous affine mean cervatures is constant and Ln≠0 0, which is a generalization of the characterization of ovaloid