Abstract
In this paper, we reformulate the Euler–Lagrange equations of Willmore surfaces in Sn as the flatness of a family of certain loop algebra–valued 1–forms. Therefore we can give the Weierstrass type representation of conformal Willmore surfaces. We also discuss the relations between conformal Willmore surfaces in Sn and minimal surfaces in constant curvature spaces Sn, Rn, Hn, and prove that some special Willmore surfaces can be derived from minimal surfaces in Sn, Rn, Hn.
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