Bi-Lagrangian structures and the space of rays
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929414612189184 |
|---|---|
| author | Domitrz, Wojciech Zubilewicz, Marcin |
| author_facet | Domitrz, Wojciech Zubilewicz, Marcin |
| contents | This paper focuses on local curvature invariants associated with bi-Lagrangian structures. We establish several geometric conditions that determine when the canonical connection is flat, building on our previous findings regarding divergence-free webs. Addressing questions raised by Tabachnikov, we provide complete solutions to two problems: the existence of flat bi-Lagrangian structures within the space of rays induced by a pair of hypersurfaces, and the existence of flat bi-Lagrangian structures induced by tangents to Lagrangian curves in the symplectic plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bi-Lagrangian structures and the space of rays Domitrz, Wojciech Zubilewicz, Marcin Differential Geometry 53A60, 53D12, 78A05 This paper focuses on local curvature invariants associated with bi-Lagrangian structures. We establish several geometric conditions that determine when the canonical connection is flat, building on our previous findings regarding divergence-free webs. Addressing questions raised by Tabachnikov, we provide complete solutions to two problems: the existence of flat bi-Lagrangian structures within the space of rays induced by a pair of hypersurfaces, and the existence of flat bi-Lagrangian structures induced by tangents to Lagrangian curves in the symplectic plane. |
| title | Bi-Lagrangian structures and the space of rays |
| topic | Differential Geometry 53A60, 53D12, 78A05 |
| url | https://arxiv.org/abs/2403.10345 |