Willmore surfaces in the four-sphere

Willmore immersions of an orientable surface X in the n-dimensionalsphere appear as the extremal points of a conformally invariant variational problem in the space of all immersions f: X S ⁿ.In this paper we will study Willmore immersions of the differentiable two-sphere in S ⁴, using the method of moving frames and Cartan's conformal structures.The work on this paper was partially supported by a Fellowship of the Consiglio Nazionale delle Ricerche.