Algebraically Special, Real Alpha Geometries

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.

27 pages; v3 of 9 Sep 2011 replaces earlier versions, correcting minor typographical errors. The published version is slightly abbreviated

References in corpus (2)

• A spinor approach to Walker geometry
• Spin coefficients for four-dimensional neutral metrics, and null geometry

Cited by in corpus (6)

• Spin coefficients for four-dimensional neutral metrics, and null geometry
• Real AlphaBeta-Geometries
• Killing Symmetries in $\mathcal{H}$-Spaces with $\Lambda$
• Null Killing vectors and geometry of null strings in Einstein spaces
• Hyperheavenly spaces and their application in Walker and para-Kähler geometries: Part I
• Hyperheavenly spaces and their application in Walker and para-Kähler geometries: part II