Construction of Willmore two-spheres via harmonic maps into $SO^+(1,n+3)/(SO^+(1,1)\times SO(n+2))$

zbMATH Open1396.53023arXiv1604.02674MaRDI QIDQ4604294

Peng Wang

Publication date: 23 February 2018

Abstract: This paper aims to provide a description of totally isotropic Willmore two-spheres and their adjoint transforms. We first recall the isotropic harmonic maps which are introduced by H'elein, Xia-Shen and Ma for the study of Willmore surfaces. Then we derive a description of the normalized potential (some Lie algebra valued meromorphic 1-forms) of totally isotropic Willmore two-spheres in terms of the isotropic harmonic maps. In particular, the corresponding isotropic harmonic maps are of finite uniton type. The proof also contains a concrete way to construct examples of totally isotropic Willmore two-spheres and their adjoint transforms. As illustrations, two kinds of examples are obtained this way.

Full work available at URL: https://arxiv.org/abs/1604.02674

zbMATH Keywords

harmonic mapsymmetric spaceWillmore surface

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometric aspects of harmonic maps (53C43) Differential geometry of symmetric spaces (53C35)

Related Items (1)

Explicit construction of harmonic two-spheres in \(SU(3)/SO(3)\)

This page was built for publication: Construction of Willmore two-spheres via harmonic maps into $SO^+(1,n+3)/(SO^+(1,1)\times SO(n+2))$

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4604294)