@article {Xia:2004-11-01T00:00:00:1439-8516:1029,
author = "Xia, Qiao and Shen, Yi",
title = "Weierstrass Type Representation of Willmore Surfaces in *S* ^{ n }",
journal = "Acta Mathematica Sinica",
volume = "20",
number = "6",
year = "2004-11-01T00:00:00",
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 }.",
pages = "1029-1046",
url = "http://www.ingentaconnect.com/content/klu/10114/2004/00000020/00000006/art00009",
doi = "doi:10.1007/s10114-004-0389-0",
keyword = "53C42, 58E20, Extended lift of a conformal Willmore immersion, Loop group, Minimal surface, Weierstrass
type representation, Willmore surfaces"
}