On Hamiltonian stationarity of twisted Lagrangian tori in ${\mathbb{C}}^2$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909815404494848 |
|---|---|
| author | Chen, Jingyi Coulibaly, Patrik |
| author_facet | Chen, Jingyi Coulibaly, Patrik |
| contents | Chekanov's exotic tori have been playing an important role in symplectic geometry as they are the only known examples of Lagrangian tori in ${\mathbb{C}}^2$ that are not Hamiltonian isotopic to a product torus. In this paper, we explore the differential geometry of a wider range of tori constructed by twisting simple closed planar curves, which include both certain product tori and Chekanov's exotic tori. In particular, we investigate the minimality of area of such twisted tori under Hamiltonian deformations and show that the only minimal twisted tori are the product ones. This tells us that Chekanov's exotic tori are not area minimal in their Hamiltonian isotopy classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hamiltonian stationarity of twisted Lagrangian tori in ${\mathbb{C}}^2$ Chen, Jingyi Coulibaly, Patrik Differential Geometry Symplectic Geometry 53C42, 53D12 Chekanov's exotic tori have been playing an important role in symplectic geometry as they are the only known examples of Lagrangian tori in ${\mathbb{C}}^2$ that are not Hamiltonian isotopic to a product torus. In this paper, we explore the differential geometry of a wider range of tori constructed by twisting simple closed planar curves, which include both certain product tori and Chekanov's exotic tori. In particular, we investigate the minimality of area of such twisted tori under Hamiltonian deformations and show that the only minimal twisted tori are the product ones. This tells us that Chekanov's exotic tori are not area minimal in their Hamiltonian isotopy classes. |
| title | On Hamiltonian stationarity of twisted Lagrangian tori in ${\mathbb{C}}^2$ |
| topic | Differential Geometry Symplectic Geometry 53C42, 53D12 |
| url | https://arxiv.org/abs/2509.25493 |