Projective Structure and Holonomy in 4-dimensional Lorentz Manifolds

Details Projective Structure and Holonomy in 4-dimensional Lorentz Manifolds Projective Structure and Holonomy in 4-dimensional Lorentz Manifolds

2010-06-25

arxiv.org/abs/1006.5023v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages

Scientific paper

This paper studies the situation when two 4-dimensional Lorentz manifolds (that is, space-times) admit the same (unparametrised) geodesics, that is, when they are projectively related. A review of some known results is given and then the problem is considered further by treating each holonomy type in turn for the space-time connection. It transpires that all holonomy possibilities can be dealt with completely except the most general one and that the consequences of two space-times being projectively related leads, in many cases, to their associated Levi-Civita connections being identical.

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