The twistor equation in Lorentzian spin geometry

2003/05/04 by Helga Baum, Baum, Helga, Felipe Leitner +1 · 3 citations
Mathematics · Physics and Astronomy · #53C15 #53C50 #Advanced Differential Geometry Research #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53C15 #msc:53C50

paper · pdf · doi:10.48550/arxiv.math/0305063

20 pages

arxiv created 2003/05/04 · openalex publication_date 2003/05/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss the twistor equation in Lorentzian spin geometry. In particular, we explain the local conformal structure of Lorentzian manifolds, which admit twistor spinors inducing lightlike Dirac currents. Furthermore, we derive all local geometries with singularity free twistor spinors that occur up to dimension 7.

Citations

• Solvable Pseudo-Riemannian Symmetric Spaces

Cited by

• Conformal Killing spinors and special geometric structures in Lorentzian geometry - a survey
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of\n low dimension
• Rigid supersymmetry, conformal coupling and twistor spinors
• A Moduli Space of the Quaternionic Hopf Surface Encodes Standard Model Physics

Related

• Twistor spinors on Lorentzian symmetric spaces
• Rigid supersymmetry, conformal coupling and twistor spinors
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• Towards a Classification of pseudo-Riemannian Geometries Admitting Twistor Spinors
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