The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would
expect from an integrable system, has many symmetries, both continuous and
discrete. One class - the so-called Legendre transformations - were introduced
by Dubrovin. They are a discrete set of symmetries between the stronger concept
of a Frobenius manifold, and are generated by certain flat vector fields. In
this paper this construction is generalized to the case where the vector field
(called here the Legendre field) is non-flat but satisfies a certain set of
defining equations. One application of this more general theory is to generate
the induced symmetry between almost-dual Frobenius manifolds whose underlying
Frobenius manifolds are related by a Legendre transformation. This also
provides a map between rational and trigonometric solutions of the WDVV
equations.Comment: 23 page
