2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110245We 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.12 pagesDifferential Geometry53B30text