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Article Dans Une Revue Letters in Mathematical Physics Année : 2019

Some examples of Dirac-harmonic maps

Bernd Ammann
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Nicolas Ginoux

Résumé

We discuss a method to construct Dirac-harmonic maps developed by J. Jost, X. Mo and M. Zhu (in J. Jost, X. Mo, M. Zhu / Some explicit constructions of Dirac-harmonic maps, J. Geom. Phys. 2009, no. 11, 1512-1527). 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 J. Jost, X.~Mo, M. Zhu / Some explicit constructions of Dirac-harmonic maps, J. Geom. Phys. 2009, no. 11, 1512-1527), 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.
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Dates et versions

hal-01881638 , version 1 (26-09-2018)
hal-01881638 , version 2 (12-04-2019)

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Bernd Ammann, Nicolas Ginoux. Some examples of Dirac-harmonic maps. Letters in Mathematical Physics, 2019, 109 (5), p 1205-1218. ⟨10.1007/s11005-018-1134-4⟩. ⟨hal-01881638v2⟩
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