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 con...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.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10271106)the Education Hall of Zhejiang Province(No.20030342)
文摘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.
