in the opposite direction and consider a manifold with a commutative, associative algebra structure and a symmetric, non-degenerate bilinear form on each tangent space. Under certain conditions such a manifold in special local coordinates, called the [*flat coordinates*]{}, can be described by a solution $F$ of the WDVV equations, satisfying property . The conditions, needed for the existence of a function $F$, were systematically studied by B. Dubrovin [@Dub96; @Dub99], who called manifolds, satisfying these conditions, [*Frobenius manifolds*]{}. The function $F$ is then called a [*Frobenius manifold potential*]{}. The bilinear form is traditionally called a [*metric*]{}.

In his fundamental works [@Sai82; @Sai83] K. Saito constructed a flat metric on the parameter space of a universal unfolding of any simple singularity. B. Dubrovin [@Dub98] then proved that together with a certain commutative, associative algebra structure on each tangent space this metric defines a Frobenius manifold structure on the parameter space of the universal unfolding. These Frobenius manifolds are often called the [*Saito Frobenius manifolds*]{}. Remarkably, the same Frobenius manifolds appear in the study of the geometry of the moduli spaces of algebraic curves with certain additional structures, the so-called Fan–Jarvis–Ruan–Witten (FJRW) theory [@FJR13]. This is one of the manifestations of mirror 