On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915329941176320 |
|---|---|
| author | Vizarreta, E. Chuño Mencattini, I. Pedroni, M. |
| author_facet | Vizarreta, E. Chuño Mencattini, I. Pedroni, M. |
| contents | In this note we first characterize Poisson quasi-Nijenhuis structures on three-dimensional oriented manifolds whose underlying Poisson tensor never vanishes. We then apply this result to show that each of these structures is (locally) a deformation of a PN structure and is involutive. Finally, we prove that every such three-dimensional Poisson quasi-Nijenhuis manifold is a Haantjes manifold and that it carries a generalized Lenard-Magri chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures Vizarreta, E. Chuño Mencattini, I. Pedroni, M. Differential Geometry 37J35, 53D17, 70H06 In this note we first characterize Poisson quasi-Nijenhuis structures on three-dimensional oriented manifolds whose underlying Poisson tensor never vanishes. We then apply this result to show that each of these structures is (locally) a deformation of a PN structure and is involutive. Finally, we prove that every such three-dimensional Poisson quasi-Nijenhuis manifold is a Haantjes manifold and that it carries a generalized Lenard-Magri chain. |
| title | On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures |
| topic | Differential Geometry 37J35, 53D17, 70H06 |
| url | https://arxiv.org/abs/2502.16559 |