• Corpus ID: 119235578

The Cauchy problem for parallel spinors as first-order symmetric hyperbolic system

  title={The Cauchy problem for parallel spinors as first-order symmetric hyperbolic system},
  author={Andree Lischewski},
  journal={arXiv: Differential Geometry},
We prove that a smooth Riemannian manifold admitting an imaginary generalized Killing spinor whose Dirac current satisfies an additional algebraic constraint condition can be embedded as spacelike Cauchy hypersurface in a smooth Lorentzian manifold on which the given spinor extends to a null parallel spinor. This is in contrast to a corresponding Cauchy problem for real generalized Killing spinors into Riemannian manifolds. The construction is based on first order symmetric hyperbolic PDE… 
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