Communications in Mathematical Physics

, Volume 320, Issue 1, pp 173–198 | Cite as

The Cauchy Problems for Einstein Metrics and Parallel Spinors

  • Bernd Ammann
  • Andrei Moroianu
  • Sergiu Moroianu


The restriction of a parallel spinor on some spin manifold \({\mathcal{Z}}\) to a hypersurface \({M \subset \mathcal{Z}}\) is a generalized Killing spinor on M. We show, conversely, that in the real analytic category, every spin manifold (M, g) carrying a generalized Killing spinor ψ can be isometrically embedded as a hypersurface in a spin manifold carrying a parallel spinor whose restriction to M is ψ. We also answer negatively the corresponding question in the smooth category.


Manifold Cauchy Problem Dirac Operator Killing Spinor Einstein Metrics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bernd Ammann
    • 1
  • Andrei Moroianu
    • 2
  • Sergiu Moroianu
    • 3
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Université de Versailles-St Quentin, Laboratoire de Mathématiques, UMR 8100 du CNRSVersaillesFrance
  3. 3.Institutul de Matematică al Academiei RomâneBucharestRomania

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