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math-ph2026
Haantjes torsion and integrability: a proof of Bolsinov-Konyaev-Matveev's conjecture
Alessandro Arsie, Paolo Lorenzoni
We prove a conjecture formulated by Bolsinov, Konyaev and Matveev in [7] stating that, integrability of a system of hydrodynamic type with $\mathfr…
math-ph2026
Cyclic F-manifolds, distinguished connections and integrability
Alessandro Arsie, Paolo Lorenzoni
We show that the geometry of Hertling-Manin F-manifolds provide the appropriate theoretical framework for studying the integrability of quasilinear systems of first-o…
math-ph2026
Gibbons-Tsarev type systems and Eventual identities
Alessandro Arsie, Paolo Lorenzoni, Sara Perletti +1
We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple -manifolds cannot exist. The proof is based on the derivation and study of…