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Twistor spinors and gravitational instantons. (English) Zbl 0860.53029
The authors construct a complete Riemannian metric on the four-dimensional real vector space \(R\) which carries a two-dimensional space of twistor spinors having a common zero point. This metric is half conformally flat, but not conformally flat. Their construction uses a conformal completion at infinity of the Eguchi-Hanson metric on the exterior of a closed ball in \(R\). Contents include: an introduction; the Eguchi-Hanson metric; half-conformally flat metrics admitting twistor spinors with zeros. The paper concludes with a list of references containing twenty items.

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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