A spinor approach to Walker geometry

Details A spinor approach to Walker geometry A spinor approach to Walker geometry

2006-12-27

arxiv.org/abs/math/0612804v4

Communications in Mathematical Physics 282 (3), 577-623, 2008

Mathematics

Differential Geometry

41 pages. Typos which persisted into published version corrected, notably at (2.15)

Scientific paper

10.1007/s00220-008-0561-y

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.

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