Willmore Tori in a wide family of conformal structures on odd dimensional spheres

We obtain a variable reduction principle for the Willmore variational problem in an ample class of conformal structures on S2n+1. This variational problem is transformed into another one, associated with an elastic-energy functional with potential, on spaces of curves in CP n. Then, we give a simple method to construct Willmore tori in certain conformal structures on S2n+1. Moreover, we exhibit some families of Willmore tori for the standard conformal class on S3 and S7