From hyperheavenly spaces to Walker and Osserman spaces: II

Abstract

Spinorial formalism employed in the weak hyperheavenly space theory is used to study Osserman spaces. General forms of metrics of signature (+ + − −) for self-dual pointwise Osserman, globally Osserman and globally Jordan–Osserman spaces admitting a two-dimensional totally null self-dual integrable distribution are found by searching for solutions to respective hyperheavenly equations with Λ. As is shown the metrics obtained describe locally all self-dual pointwise Osserman, globally Osserman and globally Jordan–Osserman spaces of types II, III, N, 0 and D (where in the case of type D one assumes that the multiple undotted Penrose spinors are real).