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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| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
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irk-123456789-1468162019-02-12T01:24:10Z Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction Calderbank, D.M.J. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146816 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Calderbank, D.M.J. |
| spellingShingle |
Calderbank, D.M.J. Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calderbank, D.M.J. |
| author_sort |
Calderbank, D.M.J. |
| title |
Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT calderbankdmj selfdual4manifoldsprojectivesurfacesandthedunajskiwestconstruction |
| first_indexed |
2023-05-20T17:25:42Z |
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2023-05-20T17:25:42Z |
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1796153269760819200 |