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arXiv · 0808.2082

Algebraically Special, Real Alpha Geometries

Peter R. Law·Yasuo Matsushita
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Abstract

We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of alpha-planes (algebraically special real alpha-geometry). In particular, we determine the behaviour of (four-dimensional neutral) Walker geometry under conformal rescalings and provide a derivation of the hyperheavenly equation from conformal rescaling formulae.

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Peter R. Law, Yasuo Matsushita. 2008-08-15. Algebraically Special, Real Alpha Geometries. https://doi.org/10.1016/j.geomphys.2011.06.002

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