On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension

Abstract It is known that in low dimensions Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations can be rewritten as commuting quasilinear bi‐Hamiltonian systems. We extend some of these results to arbitrary dimension and arbitrary scalar product . In particular, we show that suitable subsets of WDVV equations can be interpreted as a set of linear line congruences in suitable Plücker embeddings. This form leads to their representation as Hamiltonian systems of conservation laws. Moreover, we show that WDVV equations can be reduced to an orthonomic form, which is also passive in low dimensions . This also leads to the commutativity of the Hamiltonian systems of conservation laws (), after which we can find a solution of the WDVV equations from a joint solution of the Hamiltonian systems. Finally, we conjecture that passivity holds in all dimensions.