Harmonic tori in De Sitter spaces \(S^{2n}_1\)

Abstract

We show that all superconformal harmonic immersions from genus one surfaces into de Sitter spaces \(S^{2n}_{1}\) with globally defined harmonic sequence are of finite-type and hence result merely from solving a pair of ordinary differential equations. As an application, we prove that all Willmore tori in \(S^{3}\) without umbilic points can be constructed in this simple way.

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Notes

  1. 1.

    Observe that whether \(c_0 \prod _{j = 1}^{N} c_{j}^{m_j}\) is a non-zero constant is independent of the choice of root vectors.

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Correspondence to Emma Carberry.

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Carberry, E., Turner, K. Harmonic tori in De Sitter spaces \(S^{2n}_1\) . Geom Dedicata 170, 143–155 (2014). https://doi.org/10.1007/s10711-013-9873-y

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Keywords

  • Harmonic maps of surfaces
  • Willmore surfaces
  • Harmonic maps and integrable systems
  • Toda equations

Mathematics Subject Classification

  • 53C43