ar X iv : m at h / 06 12 80 4 v 4 [ m at h . D G ] 7 A pr 2 00 9 A Spinor Approach to Walker Geometry
نویسنده
چکیده
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 Plebañski [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.
منابع مشابه
ar X iv : m at h / 06 12 80 4 v 3 [ m at h . D G ] 1 7 A ug 2 00 8 A Spinor Approach to Walker Geometry
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...
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