The Inversion Symmetry of the WDVV Equations and Tau Functions

Details The Inversion Symmetry of the WDVV Equations and Tau Functions The Inversion Symmetry of the WDVV Equations and Tau Functions

2010-12-28

arxiv.org/abs/1012.5708v1

Mathematics

Differential Geometry

26 pages. This is a rewritten of an early preprint arXiv: 1002.0034 with a proof of Conjecture 6.1

Scientific paper

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.

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