Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

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.

Comments: 23 pages, LaTeX; typos corrected, page 9 last line corrected to $g^{\prime }=e^{2\chi }{a}^{-1}$

References in corpus (1)

• The principle of equivalence and projective structure in space-times