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Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor

Robert L. Bryant
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Abstract

I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequence of the existence of a nontrivial parallel spinor field).

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Robert L. Bryant. 2000-04-11. Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor. https://arxiv.org/abs/math/0004073

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