论文标题
欧几里得空间中的完整$ 3 $二维自我撕裂者的分类$ \ mathbb r^{4}
A classification of complete $3$-dimensional self-shrinkers in the Euclidean space $\mathbb R^{4}$
论文作者
论文摘要
在本文中，我们将$ 3 $二维的完整自我撕裂器与恒定的norm $ s $的第二个基本形式的常规$ s $和恒定的$ f_ {3} $中的euclidean Space $ \ mathbb r^{4} $，其中$ h_ {ij} $是第二个基本形式的组成部分， $ s = \ sum_ {i，j} h^{2} _ {ij} $和$ f_ {3} = \ sum_ {i，j，j，k} h_ {ij} h_ {jk} h_ {jk} h_ {ki {ki} $。
In this paper, we completely classify $3$-dimensional complete self-shrinkers with constant norm $S$ of the second fundamental form and constant $f_{3}$ in Euclidean space $\mathbb R^{4}$, where $h_{ij}$ are components of the second fundamental form, $S=\sum_{i,j}h^{2}_{ij}$ and $f_{3}=\sum_{i,j,k}h_{ij}h_{jk}h_{ki}$.
