A note on the relationship between rational and trigonometric solutions of the WDVV equations

Details A note on the relationship between rational and trigonometric solutions of the WDVV equations A note on the relationship between rational and trigonometric solutions of the WDVV equations

2006-05-02

arxiv.org/abs/nlin/0605005v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages

Scientific paper

Legendre transformations provide a natural symmetry on the space of solutions to the WDVV equations, and more specifically, between different Frobenius manifolds. In this paper a twisted Legendre transformation is constructed between solutions which define the corresponding dual Frobenius manifolds. As an application it is shown that certain trigonometric and rational solutions of the WDVV equations are related by such a twisted Legendre transform.

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