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Weierstrass Type Representation of Willmore Surfaces in S n

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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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China

    Qiao Ling Xia & Yi Bing Shen

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  1. Qiao Ling Xia
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  2. Yi Bing Shen
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Correspondence to Qiao Ling Xia.

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

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Xia, Q.L., Shen, Y.B. Weierstrass Type Representation of Willmore Surfaces in S n . Acta Math Sinica 20, 1029–1046 (2004). https://doi.org/10.1007/s10114-004-0389-0

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  • DOI: https://doi.org/10.1007/s10114-004-0389-0

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