The Inversion Symmetry of the WDVV Equations and Tau Functions

Abstract

For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a reciprocal transformation, and the tau functions of the hierarchies are related by a Legendre type transformation. We also consider relationships between the Virasoro constraints and the topological deformations of the principal hierarchies.

28 pages. This is a rewritten of an early preprint arXiv: 1002.0034 with a proof of Conjecture 6.1. V2: The published version

References in corpus (1)

• Reciprocal transformations and local Hamiltonian structures of hydrodynamic type systems

Cited by in corpus (1)

• Polynomial Modular Frobenius Manifolds