= Parallel spinor
{title2=$\nabla\epsilon=0$}
A parallel <spinor field> is annihilated by the <spinor covariant derivative>. Its value at one point determines it on a connected domain by <parallel transport>. The <spinor curvature identity> implies $R_{\mu\nu AB}\gamma^{AB}\epsilon=0$, but this local condition alone need not settle global existence: the <spin structure> and <holonomy> also matter. Lorentzian parallel spinors need not force the whole <Ricci tensor> to vanish, unlike the positive-definite case.
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