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Twistor Spinors with Zero on Lorentzian 5-Space

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Abstract

We present in this paper a C 1-metric of Lorentzian signature (1,4) on an open neighbourhood of the origin in \(\mathbb{R}^{5}\), which 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 and the associated conformal Killing vector to the twistor generates a one-parameter group of essential conformal transformations. The construction is based on the Eguchi-Hanson metric in dimension 4.

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Authors and Affiliations

  1. Institut für Geometrie und Topologie, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Felipe Leitner

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  1. Felipe Leitner
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Correspondence to Felipe Leitner.

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Communicated by G.W. Gibbons

The research in this work was supported by a Junior Research Fellowship grant of the Erwin-Schrödinger-International (ESI) Institute in Vienna financed by the Austrian Ministry of Education, Science and Culture (BMBWK) and by a fellowship grant of the Sonderforschungsbereich 647’ Space-Time-Matter - Geometric and Analytic Structures’ of the Deutsche Forschungsgemeinschaft (DFG) at Humboldt University Berlin.

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Leitner, F. Twistor Spinors with Zero on Lorentzian 5-Space. Commun. Math. Phys. 275, 587–605 (2007). https://doi.org/10.1007/s00220-007-0326-z

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  • DOI: https://doi.org/10.1007/s00220-007-0326-z

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