Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction
I present a construction of real or complex selfdual conformal 4-manifolds (of signature (2,2) in the real case) from a natural gauge field equation on a real or complex projective surface, the gauge group being the group of diffeomorphisms of a real or complex 2-manifold. The 4-manifolds obtained a...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146816 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction / D.M.J. Calderbank // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862701021579444224 |
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| author | Calderbank, D.M.J. |
| author_facet | Calderbank, D.M.J. |
| citation_txt | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction / D.M.J. Calderbank // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | I present a construction of real or complex selfdual conformal 4-manifolds (of signature (2,2) in the real case) from a natural gauge field equation on a real or complex projective surface, the gauge group being the group of diffeomorphisms of a real or complex 2-manifold. The 4-manifolds obtained are characterized by the existence of a foliation by selfdual null surfaces of a special kind. The classification by Dunajski and West of selfdual conformal 4-manifolds with a null conformal vector field is the special case in which the gauge group reduces to the group of diffeomorphisms commuting with a vector field, and I analyse the presence of compatible scalar-flat Kähler, hypercomplex and hyperkähler structures from a gauge-theoretic point of view. In an appendix, I discuss the twistor theory of projective surfaces, which is used in the body of the paper, but is also of independent interest.
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| first_indexed | 2025-12-07T16:40:45Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146816 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:40:45Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Calderbank, D.M.J. 2019-02-11T16:18:28Z 2019-02-11T16:18:28Z 2014 Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction / D.M.J. Calderbank // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A30; 32L25; 37K25; 37K65; 53C25; 70S15; 83C20; 83C60 DOI:10.3842/SIGMA.2014.035 https://nasplib.isofts.kiev.ua/handle/123456789/146816 I present a construction of real or complex selfdual conformal 4-manifolds (of signature (2,2) in the real case) from a natural gauge field equation on a real or complex projective surface, the gauge group being the group of diffeomorphisms of a real or complex 2-manifold. The 4-manifolds obtained are characterized by the existence of a foliation by selfdual null surfaces of a special kind. The classification by Dunajski and West of selfdual conformal 4-manifolds with a null conformal vector field is the special case in which the gauge group reduces to the group of diffeomorphisms commuting with a vector field, and I analyse the presence of compatible scalar-flat Kähler, hypercomplex and hyperkähler structures from a gauge-theoretic point of view. In an appendix, I discuss the twistor theory of projective surfaces, which is used in the body of the paper, but is also of independent interest. This paper is a contribution to the Special Issue on Progress in Twistor Theory. The full collection is available
 at http://www.emis.de/journals/SIGMA/twistors.html. 
 I am extremely grateful to Maciej Dunajski and Simon West for introducing me to their stimulating
 work, and for several helpful comments. I also thank the EPSRC for financial support in
 the form of an Advanced Research Fellowship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction Article published earlier |
| spellingShingle | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction Calderbank, D.M.J. |
| title | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| title_full | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| title_fullStr | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| title_full_unstemmed | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| title_short | Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| title_sort | selfdual 4-manifolds, projective surfaces, and the dunajski-west construction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146816 |
| work_keys_str_mv | AT calderbankdmj selfdual4manifoldsprojectivesurfacesandthedunajskiwestconstruction |