TY - JOUR

T1 - Selfdual 4-manifolds, projective surfaces, and the Dunajski-west construction?

AU - Calderbank, D.M.J.

PY - 2014/3/28

Y1 - 2014/3/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84897483392&partnerID=8YFLogxK

UR - http://dx.doi.org/10.3842/SIGMA.2014.035

U2 - 10.3842/SIGMA.2014.035

DO - 10.3842/SIGMA.2014.035

M3 - Article

AN - SCOPUS:84897483392

SN - 1815-0659

VL - 10

JO - SIGMA: Symmetry, Integrability and Geometry: Methods and Applications

JF - SIGMA: Symmetry, Integrability and Geometry: Methods and Applications

ER -