Algebraically Special, Real Alpha Geometries
Differential Geometry
2011-09-13 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0808.2082,
title = {Algebraically Special, Real Alpha Geometries},
author = {Peter R. Law and Yasuo Matsushita},
journal= {arXiv preprint arXiv:0808.2082},
year = {2011}
}
Comments
27 pages; v3 of 9 Sep 2011 replaces earlier versions, correcting minor typographical errors. The published version is slightly abbreviated