Metrisability of three-dimensional path geometries
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Dunajski, M
Eastwood, M
Abstract
Given a projective structure on a three-dimensional manifold, we find explicit obstructions to the local existence of a Levi-Civita connection in the projective class. These obstructions are given by projectively invariant tensors algebraically constructed from the projective Weyl curvature. We show, by examples, that their vanishing is necessary but not sufficient for local metrisability.
Description
Keywords
math.DG, math.DG, hep-th, math-ph, math.MP, 53A20
Journal Title
European Journal of Mathematics
Conference Name
Journal ISSN
2199-675X
2199-6768
2199-6768
Volume Title
2
Publisher
Springer Science and Business Media LLC
Publisher DOI
Sponsorship
Science and Technology Facilities Council