Walker's theorem without coordinates

Andrzej Derdzinski (Department of Mathematics; Computer Science; The Ohio State University); Witold Roter (Institute of Mathematics; Wroclaw University of Technology)

REVIEW

Walker's theorem without coordinates

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0603440 v1 pith:FM7UOJCA submitted 2006-03-17 math.DG

Walker's theorem without coordinates

Andrzej Derdzinski (Department of Mathematics , The Ohio State University) , Witold Roter (Institute of Mathematics , Computer Science , Wroclaw University of Technology) This is my paper

classification math.DG

keywords walkerbundlecoordinatesfibremanifoldpseudo-riemanniantheoremaffine

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original 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.

Walker's theorem without coordinates

discussion (0)