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Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds
- Source :
- SIGMA 5 (2009), 066, 23 pages
- Publication Year :
- 2009
-
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.<br />Comment: Comments: 23 pages, LaTeX; typos corrected, page 9 last line corrected to $g'=e^{2\chi}a^{-1}$
- Subjects :
- Mathematics - Differential Geometry
General Relativity and Quantum Cosmology
Subjects
Details
- Database :
- arXiv
- Journal :
- SIGMA 5 (2009), 066, 23 pages
- Publication Type :
- Report
- Accession number :
- edsarx.0906.5227
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3842/SIGMA.2009.066