Are all Dirac-harmonic maps uncoupled?

Bernd Ammann

Are all Dirac-harmonic maps uncoupled?

Differential Geometry 2022-09-29 v2

Authors: Bernd Ammann

Abstract

Dirac-harmonic maps $(f,\phi)$ consist of a map $f:M\to N$ and a twisted spinor $\phi\in\Gamma(\Sigma M\otimes f^*TN)$ and they are defined as critical points of the super-symmetric energy functional. A Dirac-harmonic map is called \emph{uncoupled}, if $f$ is a harmonic map. We show that under some minimality assumption Dirac-harmonic maps defined on a closed domain are uncoupled.

Keywords

harmonic maps mapping theory thurston maps

Cite

@article{arxiv.2209.03074,
  title  = {Are all Dirac-harmonic maps uncoupled?},
  author = {Bernd Ammann},
  journal= {arXiv preprint arXiv:2209.03074},
  year   = {2022}
}

Comments

see also https://www.berndammann.de/publications/diracharm3 . In version2, some notation was adapted to the standards, which also implied to change the title. In version 1, a boundary term was neglected in Theorem 5 in Section 3. This Section 3 would have needed several modifications and thus was removed in version 2

Are all Dirac-harmonic maps uncoupled?

Abstract

Keywords

Cite

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