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arXiv · 0906.5227

Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

Graham S. Hall·David P. Lonie
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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.

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BibTeXRIS

Graham S. Hall, David P. Lonie. 2009-08-12. Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds. https://doi.org/10.3842/sigma.2009.066

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