Lagrangian Translating Solitons and Special Lagrangians in $\mathbb{C}^m$ with Symmetries
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911033711394816 |
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| author | Su, Wei-Bo Wood, Albert |
| author_facet | Su, Wei-Bo Wood, Albert |
| contents | We construct novel families of exact immersed and embedded Lagrangian translating solitons and special Lagrangian submanifolds in $\mathbb{C}^m$ that are invariant under the action of various admissible compact subgroups $G \leq \text{SU}(m-1)$ with cohomogeneity-two. These examples are obtained via an Ansatz generalising a construction of Castro-Lerma in $\mathbb{C}^2$. We give explicit examples of admissible group actions, including a full classification for $G$ simple. We also describe novel Lagrangian translators symmetric with respect to non-compact subgroups of the affine special unitary group $\text{SU}(m)\ltimes \mathbb{C}^m$, including cohomogeneity-one examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lagrangian Translating Solitons and Special Lagrangians in $\mathbb{C}^m$ with Symmetries Su, Wei-Bo Wood, Albert Differential Geometry 35C08 53D12 (Primary) 53E10 53D20 (Secondary) We construct novel families of exact immersed and embedded Lagrangian translating solitons and special Lagrangian submanifolds in $\mathbb{C}^m$ that are invariant under the action of various admissible compact subgroups $G \leq \text{SU}(m-1)$ with cohomogeneity-two. These examples are obtained via an Ansatz generalising a construction of Castro-Lerma in $\mathbb{C}^2$. We give explicit examples of admissible group actions, including a full classification for $G$ simple. We also describe novel Lagrangian translators symmetric with respect to non-compact subgroups of the affine special unitary group $\text{SU}(m)\ltimes \mathbb{C}^m$, including cohomogeneity-one examples. |
| title | Lagrangian Translating Solitons and Special Lagrangians in $\mathbb{C}^m$ with Symmetries |
| topic | Differential Geometry 35C08 53D12 (Primary) 53E10 53D20 (Secondary) |
| url | https://arxiv.org/abs/2507.01345 |