Further heavenly metrics and their symmetries

Abstract

New developments in a continuing investigation of complex V₄’s with purely self‐dual conformal curvature are presented: (1) conformal and projective extensions of spaces with ${\mathrm{C̄}}_{\mathrm{ȦḂĊḊ}}$ =0 are discussed; (2) Killing vectors for general heavenly metrics are determined; (3) the solutions, in heavenly spaces, for (massless) D (0,s) spinor fields (in particular, the Maxwell field) are found; then (4) new examples of heavenly metrics of types G×[–] and D×[–] are provided; lastly, contraction of the D×D solutions of Plebański and Demiański to type D×[–] is performed, giving a complex prototype of the Kerr–Newman solution, and all solutions of the type N×[–] are given, which contain two arbitrary functions of two variables.