arXiv subjects

David P. Lonie

Publications and source records attributed to David P. Lonie.

2 recordsLinked to original sources

arXiv2010

Projective Structure and Holonomy in 4-dimensional Lorentz Manifolds

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.

gr-qc↗

arXiv2009

Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

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.

math.DG↗