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.
|Number of pages||23|
|Journal||Symmetry, Integrability and Geometry: Methods and Applications|
|Publication status||Published - 2009|
- projective structure
- Lorentz manifolds
- geodesic equivalence
Hall, G. S., & Lonie, D. P. (2009). Holonomy and Projective Equivalence in 4-dimensional Lorentz Manifolds. Symmetry, Integrability and Geometry: Methods and Applications, 5, . https://doi.org/10.3842/SIGMA.2009.066