Some explicit constructions of Dirac-harmonic maps

TL;DR

This paper provides explicit constructions of Dirac-harmonic maps between Riemannian manifolds, including cases where the map is non-harmonic or harmonic but not conformal, with non-trivial spinor components.

Contribution

It introduces new explicit examples of Dirac-harmonic maps, expanding the known classes of such maps with specific harmonicity and conformality properties.

Findings

Constructed non-trivial Dirac-harmonic maps with non-harmonic $\

Produced examples where $\

Extended the class of known Dirac-harmonic maps.

Abstract

We construct explicit examples of Dirac-harmonic maps $(\phi, \psi)$ between Riemannian manifolds $(M,g)$ and $(N,g')$ which are non-trivial in the sense that $\phi$ is not harmonic. When $\dim M=2$, we also produce examples where $\phi$ is harmonic, but not conformal, and $\psi$ is non-trivial.