We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields 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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0029-3,
author = {Georges Habib and Julien Roth},
title = {Skew Killing spinors},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {844-856},
zbl = {1246.53069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0029-3}
}
Georges Habib; Julien Roth. Skew Killing spinors. Open Mathematics, Tome 10 (2012) pp. 844-856. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0029-3/
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