On the multiple existence of superquadratic Dirac-harmonic maps into flat tori (Q2311084)

Dirac harmonic maps were introduced by \textit{Q. Chen} et al. [Math. Z. 254, No. 2, 409--432 (2006; Zbl 1103.53033)]. Here these maps are called \textit{pure} Dirac-harmonic maps. An additional non-linear interaction term is introduced and it is assumed that the underlying spin manifold is closed and that the target manifold is a flat torus. Using a variational argument the existence of Dirac-harmonic maps with superquadratic-subcritical nonlinear interaction term is shown.