论文标题
$ 4 $ - 维的刚度为$ \ Mathbb {r}^{5} $
Rigidity of $4$-dimensional complete self-shrinkers in $\mathbb{R}^{5}$
论文作者
论文摘要
我们表明，任何第二个基本形式的常数norm $ s $，$ f_ {3} = 0 $和常数$ f_ {4} $等于$ \ \ \ \ \ \ \ \ \ \ mathbb {r} $ ij，基本形式，$ s = \ sum h_ {ij}^{2} $，$ f_ {3} = \ sum h_ {ij} h_ {jk} h_ {jk} h_ {ki} $ and $ f_ {4} = \ sum h_ h_ h_ h_ {ij} h_ {ij}作为应用程序，我们获得了分类结果。
We show that any $4$-dimensional complete self-shrinker in $\mathbb{R}^{5}$ with constant squared norm $S$ of the second fundamental form, $f_{3}=0$ and constant $f_{4}$ is isometric to $\mathbb{R}^{4}$, where $h_{ij}$ are components of the second fundamental form, $S=\sum h_{ij}^{2}$, $f_{3}=\sum h_{ij}h_{jk}h_{ki}$ and $f_{4}=\sum h_{ij}h_{jk}h_{kl}h_{li}$. As an application, we obtain a classification result.
