Mathematische Annalen

, Volume 365, Issue 3–4, pp 1559–1602 | Cite as

A spinorial energy functional: critical points and gradient flow

  • Bernd Ammann
  • Hartmut Weiss
  • Frederik Witt


Let M be a compact spin manifold. On the universal bundle of unit spinors we study a natural energy functional whose critical points, if \(\dim M \ge 3\), are precisely the pairs \((g,{\varphi })\) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor \({\varphi }\). 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.



The authors thank the referees for carefully reading the manuscript which led to considerable improvements of the text.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Mathematisches Seminar der Universität KielKielGermany
  3. 3.Institut für Geometrie und Topologie der Universität StuttgartStuttgartGermany

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