A spinorial energy functional: critical points and gradient flow

Let M be a compact spin manifold. 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 prop...

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Bibliographic Details
Published inMathematische annalen Vol. 365; no. 3-4; pp. 1559 - 1602
Main Authors Ammann, Bernd, Weiss, Hartmut, Witt, Frederik
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016
Subjects
Mathematics
Mathematics and Statistics
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Summary:Let M be a compact spin manifold. 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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-015-1315-8