Dirac-harmonic maps from index theory
Bernd Ammann, Nicolas Ginoux
TL;DR
This paper establishes existence results for Dirac-harmonic maps leveraging index theory, focusing on cases where the source manifold's dimension is 1 or 2 modulo 8, with solutions where the map component is harmonic.
Contribution
It introduces index theoretical methods to prove existence of Dirac-harmonic maps, especially in low-dimensional cases, providing new insights into their structure.
Findings
Existence results for Dirac-harmonic maps in specific dimensions
Solutions with harmonic underlying maps
Application of index theory to geometric analysis
Abstract
We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the source and target manifolds is a harmonic map.
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