论文标题
$ \ mathbb {r}^4 $对称相对于超平面的封闭的拉格朗日自我撕裂者
Closed Lagrangian self-shrinkers in $\mathbb{R}^4$ symmetric with respect to a hyperplane
论文作者
论文摘要
在本文中，我们证明了$ \ mathbb {r}^4 $中的封闭的拉格朗日自我撕裂者相对于超平面而言是对称的。作为推论，我们获得了Clifford圆环的新几何表征，作为独特的嵌入式封闭的Lagrangian自我脱落器对称相对于$ \ Mathbb {r}^4 $的超平面的对称。
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 $\mathbb{R}^4$.
