Twistor spinors with zero on Lorentzian 5-space
Abstract
We present in this paper a C1-metric on an open neighbourhood of the origin in 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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