Harmonic tori in de Sitter spaces $S_1^{2n}$

Emma Carberry and Katharine Turner

Abstract

We show that all superconformal harmonic immersions from genus one surfaces into de Sitter spaces $S_1^{2n}$ 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.