Holonomy and Projective Equivalence in 4-dimensional Lorentz Manifolds

Graham S Hall, David P Lonie

Research output: Contribution to journalArticle

16 Citations (Scopus)

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 languageEnglish
Article number066
Number of pages23
JournalSymmetry, Integrability and Geometry: Methods and Applications
Volume5
DOIs
Publication statusPublished - 2009

Fingerprint

Lorentz Manifolds
Holonomy
Equivalence
Levi-Civita Connection
Holonomy Group
Curvature Tensor
Geodesic
Review

Keywords

  • projective structure
  • holonomy
  • Lorentz manifolds
  • geodesic equivalence

Cite this

Holonomy and Projective Equivalence in 4-dimensional Lorentz Manifolds. / Hall, Graham S; Lonie, David P.

In: Symmetry, Integrability and Geometry: Methods and Applications, Vol. 5, 066, 2009.

Research output: Contribution to journalArticle

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