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arXiv · 2204.11386

A classification of complete $3$-dimensional self-shrinkers in the Euclidean space $\mathbb R^{4}$

Qing-Ming Cheng·Zhi Li·Guoxin Wei
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Abstract

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 $f_{3}=\sum_{i,j,k}h_{ij}h_{jk}h_{ki}$.

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Qing-Ming Cheng, Zhi Li, Guoxin Wei. 2022-04-25. A classification of complete $3$-dimensional self-shrinkers in the Euclidean space $\mathbb R^{4}$. https://doi.org/10.1007/s11425-022-2121-7

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