Walker's theorem without coordinates

Andrzej Derdzinski; Witold Roter

doi:10.1063/1.2209167

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Walker's theorem without coordinates

Andrzej Derdzinski·Witold Roter

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Abstract

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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Andrzej Derdzinski, Witold Roter. 2006-03-17. Walker's theorem without coordinates. https://doi.org/10.1063/1.2209167

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