Twistor spinors with zero on Lorentzian 5-space

Details Twistor spinors with zero on Lorentzian 5-space Twistor spinors with zero on Lorentzian 5-space

2006-02-27

arxiv.org/abs/math/0602622v1

Mathematics

Differential Geometry

17 pages

Scientific paper

10.1007/s00220-007-0326-z

We present in this paper a $C^1$-metric on an open neighbourhood of the origin in $\RR^{5}$. The metric is of Lorentzian signature $(1,4)$ and admits a solution to the twistor equation for spinors with a unique isolated zero at the origin. The metric is not conformally flat in any neighbourhood of the origin. The construction is based on the Eguchi-Hanson metric with parallel spinors on Riemannian 4-space.

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