$F$-manifolds and integrable systems of hydrodynamic type

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.

LaTeX, 21 pages; Sections 5 and 6 completely rewritten

References in corpus (2)

• Hamiltonian structure of reductions of the Benney system
• Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type

Cited by in corpus (6)

• Dubrovin's duality for $F$-manifolds with eventual identities
• Natural connections for semi-Hamiltonian systems: The case of the $\epsilon$-system
• Some generalizations of the variety of transposed Poisson algebras
• Symmetries of F-manifolds with eventual identities and special families of connections
• Purely non-local Hamiltonian formalism, Kohno connections and $\vee$-systems
• Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation