Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

Details Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

2009-06-29

arxiv.org/abs/0906.5227v2

SIGMA 5 (2009), 066, 23 pages

Mathematics

Differential Geometry

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

Scientific paper

10.3842/SIGMA.2009.066

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.

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