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).

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'

Cited by in corpus (37)

• All supersymmetric solutions of minimal supergravity in five dimensions
• Supersymmetric black rings and three-charge supertubes
• AdS_6 solutions of type II supergravity
• The spinorial geometry of supersymmetric heterotic string backgrounds
• The spinorial geometry of supersymmetric IIB backgrounds
• Killing Spinors and SYM on Curved Spaces
• The G_2 spinorial geometry of supersymmetric IIB backgrounds
• Systematics of M-theory spinorial geometry
• Four--Dimensional Metrics Conformal to Kahler
• N=31, D=11
• M-theory compactification, fluxes and AdS_4
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality
• Refining G-structure classifications
• On the Magical Supergravities in Six Dimensions
• On the absence of BPS preonic solutions in IIA and IIB supergravities
• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• Parallelisable Heterotic Backgrounds
• Geometry of Killing spinors in neutral signature
• Supersymmetric Kaluza-Klein reductions of M-waves and MKK-monopoles
• Gravitational Instantons and Euclidean Supersymmetry
• Special Geometry and Space-time Signature
• Supersymmetric Killing Structures
• Generalized geometry of two-dimensional vacua
• Cauchy problems for Lorentzian manifolds with special holonomy
• Para-Complex Geometry and Gravitational Instantons
• Invariant Killing spinors in 11D and type II supergravities
• Parallel spinors, pp-waves, and gravitational perturbations
• Klein and Conformal Superspaces, Split Algebras and Spinor Orbits
• Higher-dimensional field theories from type II supergravity
• Spinorial Geometry and Supergravity
• Special Holonomy Manifolds in Physics
• Parallel spinors on Lorentzian Weyl spaces
• Charged Conformal Killing Spinors
• Parallel spinor flows on three-dimensional Cauchy hypersurfaces
• Quantum Klein Space and Superspace
• Decomposable $(5,6)$-solutions in eleven-dimensional supergravity
• A Moduli Space of the Quaternionic Hopf Surface Encodes Standard Model Physics