Some examples of Dirac-harmonic maps

Autor: Bernd Ammann, Nicolas Ginoux
Přispěvatelé: Universität Regensburg (UR), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), B. Ammann was partially supported by the DFG Graduiertenkolleg GRK 1692 'Curvature, Cycles, and Cohomology' and by the DFG Sonderforschungsbereich 1085 'Higher Invariants — Interactions between Arithmetic Geometry and Global Analysis'.
Rok vydání: 2018
Předmět:
Zdroj: Letters in Mathematical Physics
Letters in Mathematical Physics, Springer Verlag, 2019, 109 (5), p 1205-1218. ⟨10.1007/s11005-018-1134-4⟩
ISSN: 0377-9017
1573-0530
DOI: 10.48550/arxiv.1809.09859
Popis: 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, \emph{Some explicit constructions of Dirac-harmonic maps}, J. Geom. Phys. \textbf{59} (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, \emph{Some explicit constructions of Dirac-harmonic maps}, J. Geom. Phys. \textbf{59} (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.
Databáze: OpenAIRE
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