$F$-manifolds and integrable systems of hydrodynamic type

We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of F-manifold with compatible connection generalizing a structure introduced by Manin.

💡 Research Summary

The paper investigates the interplay between the algebraic structure of associative commutative algebras and integrable systems of hydrodynamic type, focusing on the Hertling‑Manin (HM) condition imposed on the structure constants. After a concise review of F‑manifolds, the authors recall that an F‑manifold is equipped with a multiplication on the tangent bundle whose structure constants (c^i_{jk}) satisfy the symmetry condition
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