About Twistor Spinors with Zero in Lorentzian Geometry

We describe the local conformal geometry of a Lorentzian spin manifold (M,g) admitting a twistor spinor φ with zero. Moreover, we describe the shape of the zero set of φ. If φ has isolated zeros then the metric g is locally conformally equivalent to a static monopole. In the other case the zero set...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2009
Main Author: Leitner, F.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149142
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:About Twistor Spinors with Zero in Lorentzian Geometry / F. Leitner // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Leitner, F.
author_facet Leitner, F.
citation_txt About Twistor Spinors with Zero in Lorentzian Geometry / F. Leitner // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 25 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We describe the local conformal geometry of a Lorentzian spin manifold (M,g) admitting a twistor spinor φ with zero. Moreover, we describe the shape of the zero set of φ. If φ 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 φ, which is a conformal Killing vector field, plays an important role for our discussion as well.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-11-24T04:40:31Z
publishDate 2009
publisher Інститут математики НАН України
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spelling Leitner, F.
2019-02-19T17:39:06Z
2019-02-19T17:39:06Z
2009
About Twistor Spinors with Zero in Lorentzian Geometry / F. Leitner // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 25 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 53C27; 53B30
https://nasplib.isofts.kiev.ua/handle/123456789/149142
We describe the local conformal geometry of a Lorentzian spin manifold (M,g) admitting a twistor spinor φ with zero. Moreover, we describe the shape of the zero set of φ. If φ 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 φ, which is a conformal Killing vector field, plays an important role for our discussion as well.
This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
About Twistor Spinors with Zero in Lorentzian Geometry
Article
published earlier
spellingShingle About Twistor Spinors with Zero in Lorentzian Geometry
Leitner, F.
title About Twistor Spinors with Zero in Lorentzian Geometry
title_full About Twistor Spinors with Zero in Lorentzian Geometry
title_fullStr About Twistor Spinors with Zero in Lorentzian Geometry
title_full_unstemmed About Twistor Spinors with Zero in Lorentzian Geometry
title_short About Twistor Spinors with Zero in Lorentzian Geometry
title_sort about twistor spinors with zero in lorentzian geometry
url https://nasplib.isofts.kiev.ua/handle/123456789/149142
work_keys_str_mv AT leitnerf abouttwistorspinorswithzeroinlorentziangeometry