Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor
Differential Geometry
2007-05-23 v1
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).
Cite
@article{arxiv.math/0004073,
title = {Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor},
author = {Robert L. Bryant},
journal= {arXiv preprint arXiv:math/0004073},
year = {2007}
}
Comments
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'