# A spinorial energy functional: critical points and gradient flow

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Bernd Ammann, Hartmut Weiss, Frederik Witt

**A spinorial energy functional: critical points and gradient flow**
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*Math. Ann.* **365** *1559-1602* (2016), DOI: 10.1007/s00208-015-1315-8

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M ≥ 3, are precisely the pairs (g,φ) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor φ. 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.

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The Paper was written on 16.7.2012

Last update 16.7.2012