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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146816 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| spellingShingle |
Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction Calderbank, D.M.J. |
| title_short |
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_sort |
selfdual 4-manifolds, projective surfaces, and the dunajski-west construction |
| author |
Calderbank, D.M.J. |
| author_facet |
Calderbank, D.M.J. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146816 |
| 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. |
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2025-12-07T16:40:45Z |
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