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| 摘要: |
| 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. |
| 关键词: 对称多项式 卵形面 椭球 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:国家自然科学基金项目资(11171235). |
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| A CLASS OF SYMMETRIC POLYNOMIAL AND ITS APPLICATIONS ON DIFFERENTIAL GEOMETRY |
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CAO Ran,WANG Bao-fu
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| Abstract: |
| 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. |
| Key words: symmetric polynomial ovaloid ellipsoid |
