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Mathematics > Differential Geometry

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

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).
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'
Subjects: Differential Geometry (math.DG)
MSC classes: 53A50, 53B30
Journal reference: S\'emin. Congr., 4, Soc. Math. France, Paris, 2000, 53--94
Cite as: arXiv:math/0004073 [math.DG]
  (or arXiv:math/0004073v1 [math.DG] for this version)

Submission history

From: Robert L. Bryant [view email]
[v1] Tue, 11 Apr 2000 22:09:15 GMT (49kb)