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

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.

15 pages

References in corpus (4)

• The geometric complexity of special Lagrangian $T^2$-cones
• A proof of the Willmore conjecture
• The Closure of Spectral Data for Constant Mean Curvature Tori in $S^3$
• The spectral data for Hamiltonian stationary Lagrangian tori in R^4

Cited by in corpus (1)

• Killing fields and Conservation Laws for rank-1 Toda field equations