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Some explicit constructions of Dirac-harmonic maps
Jürgen Jost, Xiaohuan Mo and Miaomiao Zhu
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.