Harmonic tori in de Sitter spaces $S^{2n}_1$

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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