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$F$ -manifolds and integrable systems of hydrodynamic type

Paolo Lorenzoni; Marco Pedroni; Andrea Raimondo — 2011

Archivum Mathematicum

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.

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F -manifolds and integrable systems of hydrodynamic type

$F$ -manifolds and integrable systems of hydrodynamic type