Walker's theorem without coordinates

Details Walker's theorem without coordinates Walker's theorem without coordinates

2006-03-17

arxiv.org/abs/math/0603440v1

J. Math. Phys. 47 (2006), no. 6, 062504, 8 pp.

Mathematics

Differential Geometry

12 pages

Scientific paper

10.1063/1.2209167

We provide a coordinate-free version of the local classification, due to A. G. Walker [Quart. J. Math. Oxford (2) 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds. The underlying manifold is realized, locally, as the total space of a fibre bundle, each fibre of which is an affine principal bundle over a pseudo-Riemannian manifold. All structures just named are naturally determined by the distribution and the metric, in contrast with the non-canonical choice of coordinates in the usual formulation of Walker's theorem.

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