Skew Killing spinors

International audienceIn 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