Projective Structure and Holonomy in 4-dimensional Lorentz Manifolds
General Relativity and Quantum Cosmology
2015-05-19 v1
Abstract
This paper studies the situation when two 4-dimensional Lorentz manifolds (that is, space-times) admit the same (unparametrised) geodesics, that is, when they are projectively related. A review of some known results is given and then the problem is considered further by treating each holonomy type in turn for the space-time connection. It transpires that all holonomy possibilities can be dealt with completely except the most general one and that the consequences of two space-times being projectively related leads, in many cases, to their associated Levi-Civita connections being identical.
Cite
@article{arxiv.1006.5023,
title = {Projective Structure and Holonomy in 4-dimensional Lorentz Manifolds},
author = {Graham S. Hall and David P. Lonie},
journal= {arXiv preprint arXiv:1006.5023},
year = {2015}
}
Comments
24 pages