WDVV-like equations in N = 2 SUSY Yang-Mills theory

The prepotential F(a_i), defining the low-energy effective action of the SU(N)N = 2 SUSY gluodynamics, satisfies an enlarged set of the WDVV-like equations F_iF^-1_k F_j = F_jF^-1_k F_i for any triple i,j , k = 1,...,N - 1, where matrix F_i is equal to (F_i)_mn =∂³F/(∂a_i∂a_m∂a_n) . The same equations are actually true for generic topological theories. In contrast to the conventional formulation, when k is restricted to k = 0, in the proposed system there is no distinguished ``first'' time-variable, and the indices can be raised with the help of any ``metric'' η^(k)_mn = (F_k)_mn, not obligatory flat. All the equations (for all i, j, k) are true simultaneously. This result provides a new parallel between the Seiberg-Witten theory of low-energy gauge models in 4d and topological theories.