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

2000/04/11 by Robert L. Bryant
Mathematics · #math.DG #msc:53A50 #msc:53B30

paper · pdf

published as Sémin. Congr., 4, Soc. Math. France, Paris, 2000, 53--94 · 40 pages, latex2e with smfart.cls and hyperref. Written for the proceedings of the June 1999 CIRM conference at Luminy, 'Analyse Harmonique et Analyse sur les Varietes'

arxiv created 2000/04/11 · arxiv updated 2009/11/30

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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