Harmonic tori in De Sitter spaces $$S^{2n}_1$$ S 1 2 n

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.