Parallel spinors and holonomy groups

Abstract

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.

10 pages, LaTeX2e

Cited by in corpus (17)

• The spinorial geometry of supersymmetric heterotic string backgrounds
• The G_2 spinorial geometry of supersymmetric IIB backgrounds
• On the full holonomy group of special Lorentzian manifolds
• A spinorial energy functional: critical points and gradient flow
• The spinorial energy functional on surfaces
• Sasakian Geometry, Holonomy, and Supersymmetry
• Geometry of Spin and Spin^c structures in the M-theory partition function
• A mass for ALF manifolds
• Bondi mass cannot become negative in higher dimensions
• Killing Vector Fields and Superharmonic Field Theories
• Spinors of real type as polyforms and the generalized Killing equation
• On Rigidly Scalar-Flat Manifolds
• A Geometric Construction of Solutions to 11D Supergravity
• Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models
• Deformations of nearly parallel G_2-structures
• Doubly Extended Lie Groups - Curvature, Holonomy and Parallel Spinors
• On the formality problem for manifolds with special holonomy