Skew Killing spinors

Abstract : In this paper, we study the existence of a skew Killing spinor (see the def\mbox{}inition below) on $2$ and $3$-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor f\mbox{}ields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.
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Submitted on : Monday, October 10, 2011 - 4:48:45 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:03 PM
Long-term archiving on : Wednesday, January 11, 2012 - 2:35:06 AM

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  • HAL Id : hal-00630695, version 1
  • ARXIV : 1110.2061

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Georges Habib, Julien Roth. Skew Killing spinors. Central European Journal of Mathematics, Springer Verlag, 2012, 10 (3), pp.844-856. ⟨hal-00630695⟩

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