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Willmore tori in the 4–Sphere with nontrivial normal bundle

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References

  1. Babich, M., Bobenko, A.: Willmore tori with umbilic lines and minimal surfaces in hyperbolic space. Duke Math. Journal 72, 151–185 (1993)

    Article  Google Scholar 

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

    Google Scholar 

  3. Burstall, F., Ferus, D., Leschke, K., Pedit, F., Pinkall, U.: Conformal geometry of surfaces in S4 and quaternions. Lecture Notes in Mathematics, Springer, Berlin, Heidelberg, 2002

  4. Eells, J., Wood, J.C.: Harmonic maps from surfaces into projective spaces. Adv. Math. 49, 217–263 (1983)

    Article  Google Scholar 

  5. Ejiri, N.: Willmore surfaces with a duality in Sn(1). Proc. Lond. Math. Soc. III Ser. 57(2), 383–416 (1988)

    Google Scholar 

  6. Ferus, D., Leschke, K., Pedit, F., Pinkall, U.: Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori. Invent. Math. Vol. 146, 507–593 (2001)

    Article  Google Scholar 

  7. Ferus, D., Pedit, F.: S1-equivariant minimal tori in S4 and S1-equivariant Willmore tori in S3. Math. Z. 204, 269–282 (1990)

    Google Scholar 

  8. Ferus, D., Pedit, F., Pinkall, U., Sterling, I.: Minimal tori in S4. J. reine angew. Math. 429, 1–47 (1992)

    Google Scholar 

  9. Hitchin, N.: Harmonic maps from a 2-torus to the 3-sphere. J. Differential Geom. 31(3), 627–710 (1990)

    Google Scholar 

  10. Montiel, S.: Willmore two-spheres in the four sphere. Trans. Am. Math. Soc. Vol. 352, 4449–4486 (2000)

    Google Scholar 

  11. Pinkall, U.: Hopf tori in S3. Invent. Math. 81(2), 379–386 (1985)

    Article  Google Scholar 

  12. Schmidt, M.: A proof of the Willmore conjecture. http://arXiv.org/abs/math.DG/0203224, 2002

  13. Willmore, T.J.: Curvature of closed surfaces in ℝ3. Actas II Coloq. Int. Geom. Diferencial, Santiago Compostela, 1968, pp. 7–9

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Correspondence to K. Leschke.

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Leschke, K., Pedit, F. & Pinkall, U. Willmore tori in the 4–Sphere with nontrivial normal bundle. Math. Ann. 332, 381–394 (2005). https://doi.org/10.1007/s00208-005-0630-x

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