Equivariant constrained Willmore tori in the 3-sphere

Abstract

In this paper we study equivariant constrained Willmore tori in the 3-sphere. These tori admit a 1-parameter group of Möbius symmetries and are critical points of the Willmore energy under conformal variations. We show that the associated spectral curve of an equivariant torus is given by a double covering of $\mathbb{C}$ and classify equivariant constrained Willmore tori by the genus g of their spectral curve. In this case the spectral genus satisfies $g\le 3.$

24 pages

References in corpus (4)

• Quaternionic holomorphic geometry: Pluecker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori
• Constrained Willmore Surfaces
• Conformal maps from a 2-torus to the 4-sphere
• The spectral curve of a quaternionic holomorphic line bundle over a 2-torus

Cited by in corpus (1)

• Constrained Willmore and CMC tori in the 3-sphere