Quasi-Frobenius algebras and their integrable N-parametric deformations generated by compatible (N x N)-metrics of constant Riemannian curvature

We prove that the description of pencils of compatible (N x N)-metrics of constant Riemannian curvature is equivalent to a special class of integrable N-parametric deformations of quasi-Frobenius (in general, noncommutative) algebras.