Address:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca Via Roberto Cozzi 53, I-20125 Milano, Italy
Dipartimento di Ingegneria dell’informazione e metodi matematici Università di Bergamo – Sede di Dalmine viale Marconi 5, I-24044 Dalmine BG, Italy
Department of Mathematics, Imperial College 180 Queen’s Gate, London SW7 2AZ, UK
E-mail:
paolo.lorenzoni@unimib.it
marco.pedroni@unibg.it
a.raimondo@imperial.ac.uk
Abstract: 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.
AMSclassification: primary 35Q35; secondary 53B05, 53D45.
Keywords: F-manifolds, Frobenius manifolds, integrable systems, PDEs of hydrodynamic type.