The cauchy problem for metrics with parallel spinors


We show that in the analytic category, given a Riemannian metric g on a hypersurface M ⊂ Z and a symmetric tensor W on M , the metric g can be locally extended to a Riemannian Einstein metric on Z with second fundamental form W , provided that g and W satisfy the constraints on M imposed by the contracted Codazzi equations. We use this fact to study the… (More)


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