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Causal conformal vector fields, and singularities of twistor spinors

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Abstract

In this paper, we study the geometry around the singularity of a twistor spinor, on a Lorentz manifold (M, g) of dimension greater or equal to three, endowed with a spin structure. Using the dynamical properties of conformal vector fields, we prove that the geometry has to be conformally flat on some open subset of any neighbourhood of the singularity. As a consequence, any analytic Lorentz manifold, admitting a twistor spinor with at least one zero has to be conformally flat.

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  1. Département de Mathématiques, Université Paris-Sud, 91405, Orsay Cedex, France

    Charles Frances

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  1. Charles Frances
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Correspondence to Charles Frances.

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Frances, C. Causal conformal vector fields, and singularities of twistor spinors. Ann Glob Anal Geom 32, 277–295 (2007). https://doi.org/10.1007/s10455-007-9060-1

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  • DOI: https://doi.org/10.1007/s10455-007-9060-1

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