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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski–West Construction
D. M. J. Calderbank Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
Аннотация:
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.
Ключевые слова:
selfduality; twistor theory; integrable systems; projective geometry.
Поступила: 21 января 2014 г.; в окончательном варианте 18 марта 2014 г.; опубликована 28 марта 2014 г.
Образец цитирования:
D. M. J. Calderbank, “Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski–West Construction”, SIGMA, 10 (2014), 035, 18 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma900 https://www.mathnet.ru/rus/sigma/v10/p35
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