oaioai:CiteSeerX.psu:10.1.1.573.4213

SELFDUAL 4-MANIFOLDS, PROJECTIVE SURFACES, AND THE DUNAJSKI–WEST CONSTRUCTION

Abstract

Abstract. 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. When the gauge group reduces to the group of diffeomorphisms commuting with a vector field, I reobtain the Dunajski–West classification of selfdual conformal 4-manifolds with a null conformal vector field. I then 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 I use in the body of the paper, but is also of independent interest

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oaioai:CiteSeerX.psu:10.1.1.573.4213Last time updated on 10/29/2017

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