Causal conformal vector fields, and singularities of twistor spinors. (English) Zbl 1126.53014
The author studies 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, he proves 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.
Reviewer: Huafei Sun (Beijing)
MSC:
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
| 53C27 | Spin and Spin\({}^c\) geometry |
| 37C10 | Dynamics induced by flows and semiflows |
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