New Frobenius structures on Hurwitz spaces in terms of Schiffer and Bergmann kernels

Abstract:
New family of flat potential (Darboux-Egoroff) metrics on the Hurwitz spaces and corresponding Frobenius structures are found. We describe new structures of Frobenius manifold on the Hurwitz spaces considered as real manifolds; our construction is inspired by that of Dubrovin who defined Frobenius structures on Hurwitz spaces considered as complex manifolds.