Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.15279 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915454712283136 |
|---|---|
| author | Chang, Shu-Cheng Wu, Chin-Tung Zhang, Liuyang Zhang, Qiuxia |
| author_facet | Chang, Shu-Cheng Wu, Chin-Tung Zhang, Liuyang Zhang, Qiuxia |
| contents | In this article, we first classify Legendrian self-shrinkers in $\mathbb{R}% ^{3}$ and $\mathbb{R}^{5}$. We then proved a Legendrian rigidity theorem, which can be regarded as an analogue of the result of Li-Wang \cite{lw}. More precisely, let $F(Σ)\subset\mathbb{R}^{5}$ be an orientable Legendrian self-shrinker, if $\Vert A\Vert_{g}^{2}\leq2$ and the associated Legendrian immersion $\bar{F}\subset\mathbb{R}^{4}\times\mathbb{S}^{1}$ is compact, then $\bar{F}$ must be a flat minimal generalized Legendrian Clifford torus in $\mathbb{S}^{5}$, whose cone $\mathcal{C}(\bar{F}(Σ))$ is the Harvey-Lawson special Lagrangian cone in $\mathbb{C}^{3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity and Classification of Legendrian Self-Shrinkers Chang, Shu-Cheng Wu, Chin-Tung Zhang, Liuyang Zhang, Qiuxia Differential Geometry 53C44, 53C56 In this article, we first classify Legendrian self-shrinkers in $\mathbb{R}% ^{3}$ and $\mathbb{R}^{5}$. We then proved a Legendrian rigidity theorem, which can be regarded as an analogue of the result of Li-Wang \cite{lw}. More precisely, let $F(Σ)\subset\mathbb{R}^{5}$ be an orientable Legendrian self-shrinker, if $\Vert A\Vert_{g}^{2}\leq2$ and the associated Legendrian immersion $\bar{F}\subset\mathbb{R}^{4}\times\mathbb{S}^{1}$ is compact, then $\bar{F}$ must be a flat minimal generalized Legendrian Clifford torus in $\mathbb{S}^{5}$, whose cone $\mathcal{C}(\bar{F}(Σ))$ is the Harvey-Lawson special Lagrangian cone in $\mathbb{C}^{3}$. |
| title | Rigidity and Classification of Legendrian Self-Shrinkers |
| topic | Differential Geometry 53C44, 53C56 |
| url | https://arxiv.org/abs/2508.15279 |