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This article is cited in 7 scientific papers (total in 7 papers)
About Twistor Spinors with Zero in Lorentzian Geometry
Felipe Leitner Universität Stuttgart, Institut für Geometrie und Topologie, Fachbereich Mathematik, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
Abstract:
We describe the local conformal geometry of a Lorentzian spin manifold $(M,g)$ admitting a twistor spinor $\phi$ with zero. Moreover, we describe the shape of the zero set of $\phi$. If $\phi$ has isolated zeros then the metric $g$ is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and $g$ is locally conformally equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an essential way. The Dirac current of $\phi$, which is a conformal Killing vector field, plays an important role for our discussion as well.
Keywords:
Lorentzian spin geometry; conformal Killing spinors; tractors and twistors.
Received: April 6, 2009; in final form July 10, 2009; Published online July 28, 2009
Citation:
Felipe Leitner, “About Twistor Spinors with Zero in Lorentzian Geometry”, SIGMA, 5 (2009), 079, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma424 https://www.mathnet.ru/eng/sigma/v5/p79
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Abstract page: | 281 | Full-text PDF : | 54 | References: | 43 |
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