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Article Dans Une Revue Annals of Global Analysis and Geometry Année : 2007

Causal conformal vector fields, and singularities of twistor spinors

Charles Frances

Résumé

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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Dates et versions

hal-03165738 , version 1 (10-03-2021)

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Charles Frances. Causal conformal vector fields, and singularities of twistor spinors. Annals of Global Analysis and Geometry, 2007, 32 (3), pp.277-295. ⟨10.1007/s10455-007-9060-1⟩. ⟨hal-03165738⟩

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