Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds
Differential Geometry
2009-08-12 v2 General Relativity and Quantum Cosmology
Abstract
A study is made of 4-dimensional Lorentz manifolds which are projectively related, that is, whose Levi-Civita connections give rise to the same (unparameterised) geodesics. A brief review of some relevant recent work is provided and a list of new results connecting projective relatedness and the holonomy type of the Lorentz manifold in question is given. This necessitates a review of the possible holonomy groups for such manifolds which, in turn, requires a certain convenient classification of the associated curvature tensors. These reviews are provided.
Cite
@article{arxiv.0906.5227,
title = {Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds},
author = {Graham S. Hall and David P. Lonie},
journal= {arXiv preprint arXiv:0906.5227},
year = {2009}
}
Comments
Comments: 23 pages, LaTeX; typos corrected, page 9 last line corrected to $g'=e^{2\chi}a^{-1}$