Minimal Lagrangian surfaces in the two-dimensional complex hyperbolic quadric via the loop group method
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909053903437824 |
|---|---|
| author | Kobayashi, Shimpei Zeng, Sihao |
| author_facet | Kobayashi, Shimpei Zeng, Sihao |
| contents | We study minimal Lagrangian surfaces in the complex hyperbolic quadric. We show that minimality of a Lagrangian surface is characterized by a loop of flat connections, which yields an associated $\mathbb S^1$-family of isometric deformations. We also establish a correspondence with spacelike maximal surfaces in anti-de Sitter $3$-space via the Gauss map. Using the resulting harmonic map into the hyperbolic two-space, we develop a DPW-type representation and construct explicit examples, including $\mathbb{R}$-equivariant and radially symmetric surfaces. In particular, under suitable conditions, the $\mathbb{R}$-equivariant family contains catenoid-type examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17876 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal Lagrangian surfaces in the two-dimensional complex hyperbolic quadric via the loop group method Kobayashi, Shimpei Zeng, Sihao Differential Geometry Primary 53C42, Secondary 53D12 We study minimal Lagrangian surfaces in the complex hyperbolic quadric. We show that minimality of a Lagrangian surface is characterized by a loop of flat connections, which yields an associated $\mathbb S^1$-family of isometric deformations. We also establish a correspondence with spacelike maximal surfaces in anti-de Sitter $3$-space via the Gauss map. Using the resulting harmonic map into the hyperbolic two-space, we develop a DPW-type representation and construct explicit examples, including $\mathbb{R}$-equivariant and radially symmetric surfaces. In particular, under suitable conditions, the $\mathbb{R}$-equivariant family contains catenoid-type examples. |
| title | Minimal Lagrangian surfaces in the two-dimensional complex hyperbolic quadric via the loop group method |
| topic | Differential Geometry Primary 53C42, Secondary 53D12 |
| url | https://arxiv.org/abs/2605.17876 |