Communications in Mathematical Physics

, Volume 320, Issue 1, pp 173–198

The Cauchy Problems for Einstein Metrics and Parallel Spinors


DOI: 10.1007/s00220-013-1714-1

Cite this article as:
Ammann, B., Moroianu, A. & Moroianu, S. Commun. Math. Phys. (2013) 320: 173. doi:10.1007/s00220-013-1714-1


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.


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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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