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| 摘要: |
| 本文研究了球空间中具有常第二基本形式模长平方S超曲面的陈猜想. 目前S的第三个间隙点取值是否为2n? 依然是一个公开性的问题. 首先我们研究了位置向量和法向量在自然坐标向量上的高度函数及其性质, 然后证明了在超曲面上存在同时具有S第一、二、三间隙点项的Simons型积分方程, 这些结果可以为解决陈猜想的研究提供全新的思考途径与求解方法. |
| 关键词: 陈猜想 高度函数 Simons型积分. |
| DOI： |
| 分类号:O186.16 |
| 基金项目: |
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| Simons-type integral and Height function in Spheres |
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gongyifan
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| Abstract: |
| This article delves Chern's conjecture for hypersurfaces with constant second fundamental form squared length ~$S$ in the spherical space. At present, determining whether the third gap point of S is 2n remaining unsolved initially. First, we investigate the height functions and their properties of the position vector and normal vector in natural coordinate vectors, and then prove the existence of a Simons-type integral formula on the hypersurface that simultaneously includes the first, second, and third gap point terms of $S$. These results can provide new avenues of thought and methods for solving Chern's conjecture. |
| Key words: Chern's Conjecture Height function Simons-Type integral. |
