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
Дата:2014
Автор: Calderbank, D.M.J.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2014
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146816
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
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.
work_keys_str_mv AT calderbankdmj selfdual4manifoldsprojectivesurfacesandthedunajskiwestconstruction
first_indexed 2025-12-07T16:40:45Z
last_indexed 2025-12-07T16:40:45Z
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