Some examples of Dirac-harmonic maps
by
Bernd Ammann, Nicolas Ginoux


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Abstract

We discuss a method to construct Dirac-harmonic maps developed by J. Jost, X. Mo and M. Zhu. The method uses harmonic spinors and twistor spinors, and mainly applies to Dirac-harmonic maps of codimension 1 with target spaces of constant sectional curvature. Before the present article, it remained unclear when the conditions of the theorems in the publication by Jost, Mo and Zhu were fulfilled. We show that for isometric immersions into spaceforms, these conditions are fulfilled only under special assumptions. In several cases we show the existence of solutions.

Mathematics Subject Classification

58E20 (Primary), 53C43, 58J20, 53C27 (Secondary)

Keywords

Dirac harmonic maps, twistor spinors
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The Paper was written on 26.09.18
Last update 27.9.2018