A note on twisted Dirac operators on closed surfaces

Abstract

We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\mathrm{Spi}{\mathrm{n}}^{\mathrm{c}}$ Dirac operator. This allows us to obtain eigenvalue estimates for the twisted Dirac operator appearing in the context of Dirac-harmonic maps and their extensions, from which we also obtain several Liouville type results.

References in corpus (3)

• Liouville Theorems for Dirac-Harmonic Maps
• Some aspects of Dirac-harmonic maps with curvature term
• An estimate on the nodal set of eigenspinors on closed surfaces

Cited by in corpus (2)

• A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions
• Dirac-harmonic maps with potential