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A Spinor Approach to Walker Geometry
Authors:Peter R Law and Yasuo Matsushita
Institution:(1) 4 Mack Place, Monroe, NY 10950, USA;(2) Section of Mathematics, School of Engineering, University of Shiga Prefecture, Hikone 522-8533, Japan
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 11] and Pleba?ski 30] in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.
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