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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.25277 |
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| _version_ | 1866916044474417152 |
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| author | Arsie, Alessandro Lorenzoni, Paolo |
| author_facet | Arsie, Alessandro Lorenzoni, Paolo |
| contents | We show that Hertling-Manin F-manifolds provide the appropriate theoretical framework for studying the integrability of quasilinear systems of first-order evolutionary partial differential equations of the form ${\bf u}_t=X\circ {\bf u}_x$ under the mild assumption that $X$ is a cyclic vector field with respect to the F-product $\circ$. This approach is very general and allows us to treat even non-regular systems that were previously beyond the scope of existing techniques. Like in the regular case the information about integrability is contained in a torsionless connection associated with the system and the integrability condition reduces to a geometric condition involving the Riemann tensor of the connection and the structure functions of the product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cyclic F-manifolds, distinguished connections and integrability Arsie, Alessandro Lorenzoni, Paolo Mathematical Physics We show that Hertling-Manin F-manifolds provide the appropriate theoretical framework for studying the integrability of quasilinear systems of first-order evolutionary partial differential equations of the form ${\bf u}_t=X\circ {\bf u}_x$ under the mild assumption that $X$ is a cyclic vector field with respect to the F-product $\circ$. This approach is very general and allows us to treat even non-regular systems that were previously beyond the scope of existing techniques. Like in the regular case the information about integrability is contained in a torsionless connection associated with the system and the integrability condition reduces to a geometric condition involving the Riemann tensor of the connection and the structure functions of the product. |
| title | Cyclic F-manifolds, distinguished connections and integrability |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.25277 |