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: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| 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| _version_ | 1862531946523918336 |
|---|---|
| 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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| first_indexed | 2025-11-24T04:40:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149142 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:40:31Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |