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

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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. 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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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    Emma Carberry

  2. Department of Mathematics, 5734 S. University Avenue, Chicago, IL, 60637, USA

    Katharine Turner

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  1. Emma Carberry
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  2. Katharine Turner
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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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