Conjugate Frobenius manifold and inversion symmetry

Abstract

We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of solutions to Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations

Major revision for the first version. Title is changed, general theorem and examples are given and make use of the theory of Poisson brackets of hydrodynamic type

References in corpus (3)

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• A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of $B_n$
• Frobenius manifolds on orbits spaces