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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 066, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.066 (Mi sigma412) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

Graham S. Halla, David P. Lonieb

a Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen, AB24 3UE, Scotland, UK
b 108e Anderson Drive, Aberdeen, AB15 6BW, Scotland, UK
Full-text PDF (364 kB) Citations (18)
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DOI: https://doi.org/10.3842/SIGMA.2009.066
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.
Keywords: projective structure; holonomy; Lorentz manifolds; geodesic equivalence.
Received: March 18, 2009; in final form June 11, 2009; Published online June 29, 2009
Bibliographic databases:
Document Type: Article
MSC: 53C29; 53C22; 53C50
Language: English
Citation: Graham S. Hall, David P. Lonie, “Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds”, SIGMA, 5 (2009), 066, 23 pp.
Citation in format AMSBIB
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