Weierstrass Type Representation of Willmore Surfaces in S^n  

作　　者：Qiao Ling XIA Yi Bing SHEN 

机构地区：[1]Department of Mathematics,Zhejiang University

出　　处：《Acta Mathematica Sinica,English Series》2004年第6期1029-1046,共18页数学学报（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.10271106);the Education Hall of Zhejiang Province(No.20030342)

摘　　要：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.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.

关 键 词：Willmore surfaces Extended lift of a conformal Willmore immersion Loop group Weierstrass type representation Minimal surface 

分 类 号：O186.11[理学—数学]