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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 079, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.079
(Mi sigma424)
 

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
Full-text PDF (269 kB) Citations (7)
References:
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
Bibliographic databases:
Document Type: Article
MSC: 53C27; 53B30
Language: English
Citation: Felipe Leitner, “About Twistor Spinors with Zero in Lorentzian Geometry”, SIGMA, 5 (2009), 079, 12 pp.
Citation in format AMSBIB
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\by Felipe Leitner
\paper About Twistor Spinors with Zero in Lorentzian Geometry
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\vol 5
\papernumber 079
\totalpages 12
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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