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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| Date: | 2009 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2009
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.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| Summary: | 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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