Dirac-geodesics and their heat flows (Q889722)

The paper under review deals with the heat flows for Dirac-geodesics that are Dirac-harmonic maps from one dimensional domains. The authors establish long-time existence for the heat flows and obtain asymptotic properties of the global solution. The Dirac-geodesics on the standard 2-sphere \(S^2 (1)\) and on the hyperbolic plane \(\mathbb{H}^2\) are classified, and existence results on topological spheres and hyperbolic surfaces are derived. The solutions obtained constitute new examples of coupled Dirac-harmonic maps in the sense that the map part is not simply a harmonic map.