A spinor approach to Walker geometry
Differential Geometry
2009-04-07 v4
Abstract
A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit studies of Walker geometry and in other work of Dunajski (2002) and Plebanski (1975) in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.
Keywords
Cite
@article{arxiv.math/0612804,
title = {A spinor approach to Walker geometry},
author = {Peter R Law and Yasuo Matsushita},
journal= {arXiv preprint arXiv:math/0612804},
year = {2009}
}
Comments
41 pages. Typos which persisted into published version corrected, notably at (2.15)