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arXiv · 1207.3529

A spinorial energy functional: critical points and gradient flow

Bernd Ammann·Hartmut Weiss·Frederik Witt
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Abstract

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}. 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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Bernd Ammann, Hartmut Weiss, Frederik Witt. 2012-07-15. A spinorial energy functional: critical points and gradient flow. https://doi.org/10.1007/s00208-015-1315-8

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