On the structure of homogeneous local Poisson brackets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915272471871488 |
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| author | Carlet, Guido Casati, Matteo |
| author_facet | Carlet, Guido Casati, Matteo |
| contents | We consider an arbitrary Dubrovin-Novikov bracket of degree $k$, namely a homogeneous degree $k$ local Poisson bracket on the loop space of a smooth manifold $M$ of dimension $n$, and show that $k$ connections, defined by explicit linear combinations with constant coefficients of the standard connections associated with the Poisson bracket, are flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the structure of homogeneous local Poisson brackets Carlet, Guido Casati, Matteo Differential Geometry Mathematical Physics Exactly Solvable and Integrable Systems 53D17 (primary), 37K25 (Secondary) We consider an arbitrary Dubrovin-Novikov bracket of degree $k$, namely a homogeneous degree $k$ local Poisson bracket on the loop space of a smooth manifold $M$ of dimension $n$, and show that $k$ connections, defined by explicit linear combinations with constant coefficients of the standard connections associated with the Poisson bracket, are flat. |
| title | On the structure of homogeneous local Poisson brackets |
| topic | Differential Geometry Mathematical Physics Exactly Solvable and Integrable Systems 53D17 (primary), 37K25 (Secondary) |
| url | https://arxiv.org/abs/2505.01138 |