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Willmore surfaces in the four-sphere

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Abstract

Willmore immersions of an orientable surface X in the n-dimensionalsphere appear as the extremal points of a conformally invariant variational problem in the space of all immersions f: X → S n.

In this paper we will study Willmore immersions of the differentiable two-sphere in S 4, using the method of moving frames and Cartan's conformal structures.

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References

  1. Bryant, R.: A duality theorem for Willmore surfaces. J. Diff. Geom. 20 (1984), 23–53.

    MathSciNet  MATH  Google Scholar 

  2. Cartan, E.: Les espaces à connexion conforme. Oeuvres Completes, III, Vol. 1, 747–797.

  3. Chern, S. S.: On the minimal immersions of the two-sphere in a spaces constant curvature. In: Problems in Analysis, A Symp. in Honor of S. Bochner. Princeton University Press 1970.

  4. Jense, G. R., Rigoli, M., Yang K.: Holomorphic curves in the complex quadric. Bull. Australian Math. Soc. 35 (1987) 1, 125–148.

    Article  MathSciNet  MATH  Google Scholar 

  5. Kobayashi, S.: Transformation Groups in Differential Geometry. Berlin-Heidelberg-New York: Springer-Verlag 1972.

    Book  MATH  Google Scholar 

  6. Lawson, H. B.: Lectures in minimal submanifolds, Publish or Perish,Math. Lect. Series no. 9 (1980).

  7. Rigoli, M.: The conformal Gauss map of submanifolds in the Möbius space. Ann. Global Anal. Geom. 5 (1987) 2, 97–116.

    Article  MathSciNet  MATH  Google Scholar 

  8. Schiemangk, Ch, Sulanke, R.: Submanifolds of the Möbius space. Math. Nachr. 96, 165–183 (1980).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Università degli Studi, Istituto Matematico “U. Dini”, Viale Morgagni 67/A, I-50 134, Firenze, Italy

    Emilio Musso

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  1. Emilio Musso
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Additional information

The work on this paper was partially supported by a Fellowship of the Consiglio Nazionale delle Ricerche.

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Musso, E. Willmore surfaces in the four-sphere. Ann Glob Anal Geom 8, 21–41 (1990). https://doi.org/10.1007/BF00055016

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  • DOI: https://doi.org/10.1007/BF00055016

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