Weierstrass Type Representation of Willmore Surfaces in S n
Source: Acta Mathematica Sinica, Volume 20, Number 6, November 2004 , pp. 1029-1046(18)
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 .
Document Type: Research article
Affiliations: 1: Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China, Email: firstname.lastname@example.org 2: Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China, Email: email@example.com
Publication date: 2004-11-01