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.
Original language | English |
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Article number | 066 |
Number of pages | 23 |
Journal | Symmetry, Integrability and Geometry: Methods and Applications |
Volume | 5 |
DOIs | |
Publication status | Published - 2009 |
Keywords
- projective structure
- holonomy
- Lorentz manifolds
- geodesic equivalence