| Abstract: | In this paper, we reformulate the Euler–Lagrange equations of Willmore surfaces in S n 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 S n and minimal surfaces in constant curvature spaces S n , R n , H n , and prove that some special Willmore surfaces can be derived from minimal surfaces in S n , R n , H n . Project supported by the National Natural Science Foundation of China (No. 10271106) and the Education Hall of Zhejiang Province (No. 20030342) |
