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A spinorial energy functional: Critical points and gradient flow

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Ammann, Bernd ; Weiss, Hartmut ; Witt, Frederik
Date of publication of this fulltext: 19 Jul 2012 05:37


On the universal bundle of unit spinors we study a natural energy
functional whose critical points, if dimM C 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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