From hyperheavenly spaces to Walker and Osserman spaces: I

Physics

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Scientific paper

The notion of a weak hyperheavenly ({\cal H}{\cal H}) space is introduced and the general form of the metric for such a space is found. Spinorial connection and curvature are also calculated. It is shown that any four-dimensional Walker space is a weak nonexpanding real {\cal H}{\cal H} -space with the metric of the signature (++--) . The metrics of the self-dual Walker and the self-dual Einstein Walker spaces are given. The general form of the metric for any Walker space admitting both self-dual and anti-self-dual totally null parallel 2-distributions is found.

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