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

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

2000-04-11

arxiv.org/abs/math/0004073v1

S\'emin. Congr., 4, Soc. Math. France, Paris, 2000, 53--94

Mathematics

Differential Geometry

40 pages, latex2e with smfart.cls and hyperref. Written for the proceedings of the June 1999 CIRM conference at Luminy, 'Analy

Scientific paper

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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