A spinorial energy functional: critical points and gradient flow

Zusammenfassung

Let M be a compact spin manifold. On the universal bundle of unit spinors we study a natural energy functional whose critical points, if , are precisely the pairs consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor . We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.