Abstract
We construct a complete Riemannian metric on the four-dimensional vector space ℝ4 which carries a two-dimensional space of twistor spinor with common zero point. This metric is half-conformally flat but not conformally flat. The construction uses a conformal completion at infinity of theEguchi-Hanson metric on the exterior of a closed ball in ℝ4.
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Kühnel, W., Rademacher, HB. Twistor spinors and gravitational instantons. Lett Math Phys 38, 411–419 (1996). https://doi.org/10.1007/BF01815523
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DOI: https://doi.org/10.1007/BF01815523