$\mathbb{R}^4$ 中与超平面对称的封闭拉格朗日自收缩器

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2024-08-10 DOI:10.4310/cag.2023.v31.n8.a3

Jaehoon Lee

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引用次数: 0

摘要

在本文中，我们证明了 $\mathbb{R}^4$ 中相对于超平面对称的封闭拉格朗日自收缩物是由阿布雷斯-朗格曲线的乘积给出的。作为推论，我们得到了克利福德环作为 $\mathbb{R}^4$ 中关于超平面对称的唯一内嵌封闭拉格朗日自收缩器的新几何特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Closed Lagrangian self-shrinkers in $\mathbb{R}^4$ symmetric with respect to a hyperplane

In this paper, we prove that the closed Lagrangian self-shrinkers in $\mathbb{R}^4$ which are symmetric with respect to a hyperplane are given by the products of Abresch–Langer curves. As a corollary, we obtain a new geometric characterization of the Clifford torus as the unique embedded closed Lagrangian self-shrinker symmetric with respect to a hyperplane in $\mathbb{R}^4$.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.