On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918142923505664 |
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| author | Opanasenko, S. Vitolo, R. |
| author_facet | Opanasenko, S. Vitolo, R. |
| contents | It is known that in low dimensions WDVV equations can be rewritten as
commuting quasilinear bi-Hamiltonian systems. We extend some of these
results to arbitrary dimension $N$ and arbitrary scalar product $η$. In
particular, we show that WDVV equations can be interpreted as a set of linear
line congruences in suitable Plücker embeddings. This form leads to their
representation as Hamiltonian systems of conservation laws. Moreover, we
show that in low dimensions and for an arbitrary $η$ WDVV equations can be
reduced to passive orthonomic form. This leads to the commutativity of the
Hamiltonian systems of conservation laws. We conjecture that such a result
holds in all dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension Opanasenko, S. Vitolo, R. Exactly Solvable and Integrable Systems Mathematical Physics It is known that in low dimensions WDVV equations can be rewritten as commuting quasilinear bi-Hamiltonian systems. We extend some of these results to arbitrary dimension $N$ and arbitrary scalar product $η$. In particular, we show that WDVV equations can be interpreted as a set of linear line congruences in suitable Plücker embeddings. This form leads to their representation as Hamiltonian systems of conservation laws. Moreover, we show that in low dimensions and for an arbitrary $η$ WDVV equations can be reduced to passive orthonomic form. This leads to the commutativity of the Hamiltonian systems of conservation laws. We conjecture that such a result holds in all dimensions. |
| title | On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2509.13757 |