2014/08/10 by Maciej Dunajski, Dunajski, Maciej, Michael Eastwood +1
Mathematics · Physics and Astronomy · #53A20 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:53A20
paper · pdf · doi:10.48550/arxiv.1408.2170
19 pages. In this version we analyse the projective structures arising from Einstein-Weyl geometries and make several other minor modifications and additions
arxiv created 2014/09/06 · arxiv updated 2014/10/21
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.