On the bi-Hamiltonian Geometry of WDVV Equations

Abstract

We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove that these systems possess a compatible pair of local homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and third order, respectively).

21 pages, revised published version; exposition substantially improved

References in corpus (1)

• Projective-geometric aspects of homogeneous third-order Hamiltonian operators

Cited by in corpus (1)

• Towards the classification of homogeneous third-order Hamiltonian operators