# The Cauchy problem for metrics with parallel spinors

by

Bernd Ammann, Andrei Moroianu, Sergiu Moroianu

**The Cauchy problem for metrics with parallel spinors**
(.ps,.ps.gz or .pdf)

*Commun. Math. Phys.* **320** *173-198* (2013),

http://dx.doi.org/10.1007/s00220-013-1714-1

We show that in the analytic category, given a Riemannian metric g on a hypersurface M in 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 Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in a previous article by Bär-Gauduchon-Moroianu. We also answer negatively the corresponding questions in the smooth category.

Zurück zur Homepage

The Paper was written on 1.12.2011

Last update 21.11.2012