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This paper aims to provide a description of totally isotropic Willmoretwo-spheres and their adjoint transforms. We first recall the isotropicharmonic maps which are introduced by H\'elein, Xia-Shen and Ma for the studyof Willmore surfaces. Then we derive a description of the normalized potential(some Lie algebra valued meromorphic 1-forms) of totally isotropic Willmoretwo-spheres in terms of the isotropic harmonic maps. In particular, thecorresponding isotropic harmonic maps are of finite uniton type. The proof alsocontains a concrete way to construct examples of totally isotropic Willmoretwo-spheres and their adjoint transforms. As illustrations, two kinds ofexamples are obtained this way.

Construction of Willmore two-spheres via harmonic maps into $SO^+(1,n+3)/(SO^+(1,1)\times SO(n+2))$