Geometriae Dedicata

, Volume 170, Issue 1, pp 143–155 | Cite as

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

Original Paper

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.

Keywords

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

Mathematics Subject Classification

53C43 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  2. 2.Department of MathematicsChicagoUSA

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