在产品空间中,对于封闭的线性Weingarten子多元体的整数不等式
Fábio R Dos Santos1, Sylvia F DA Silva1, Antonio F DE Sousa1
1Universidade Federal de Pernambuco, Departamento de Matemática, Av. Jornalista Anibal Fernandes, s/n, Cidade Universitária, 50740-540 Recife, PE, Brazil.
Anais da Academia Brasileira de Ciencias
|November 1, 2023
概括
这项研究确立了产品空间中特定子数组的整体不平等. 这项研究表明,不平等的
科学领域:
- 不同几何学微分几何学
- 几何分析 几何分析
- 拓学的拓学
背景情况:
- 我们探讨了几何空间中子数组的积分不等式.
- 在微分几何学中,了解具有平行规范平均曲率向量场 (pnmc lw-submanifolds) 的子多元的属性至关重要.
- 像M_n(c) x R这样的产品空间提供了复杂的几何设置,用于研究子多元行为.
研究的目的:
- 为了获得封闭的线性Weingarten m-submanifolds与平行规范平均曲率向量场 (pnmc lw-submanifolds) 的新型积分不等式.
- 调查这种不平等的尖性,并确定平等存在的特定几何配置.
- 将分析扩展到不同的空间形式 (c = 1 和 c = -1) 和特定尺寸 (m = 2,3,和 m >= 4).
主要方法:
- 使用整微积分和几何分析技术.
- 应用平均曲率和平行向量场的概念.
- 分析产品空间M_n(c) x R.内的子多元的属性.
主要成果:
- 对于pnmc lw-submanifolds在M_n(c) x R (n > m >= 4) 中建立了一个积分不等式.
- 对于c = 1,完全带的超表面和特定的标准产品可以达到不等式的度.
- 对于c = -1,度仅通过完全带的超表面来实现.
结论:
- 导出的积分不等式为pnmc lw-submanifolds提供了一个新的几何约束.
- 对平等案例的分析揭示了优化不平等的特定几何结构.
- 这些发现有助于更深入地了解产品空间中的子方形几何学.
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