Geodesic
$F$-manifolds and integrable systems of hydrodynamic type
Archivum mathematicum, Tome 47 (2011) no. 3, pp. 163-180.

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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.
Classification : 35Q35, 53B05, 53D45
Keywords: F-manifolds; Frobenius manifolds; integrable systems; PDEs of hydrodynamic type 
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     author = {Lorenzoni, Paolo and Pedroni, Marco and Raimondo, Andrea},
     title = {$F$-manifolds and integrable systems of hydrodynamic type},
     journal = {Archivum mathematicum},
     pages = {163--180},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2011},
     mrnumber = {2852379},
     zbl = {1249.35267},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2011__47_3_a0/}
}
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Lorenzoni, Paolo; Pedroni, Marco; Raimondo, Andrea. $F$-manifolds and integrable systems of hydrodynamic type. Archivum mathematicum, Tome 47 (2011) no. 3, pp. 163-180. http://geodesic.mathdoc.fr/item/ARM_2011__47_3_a0/