### Abstract

This paper considers four-dimensional manifolds upon which there is a Lorentz metric It and a symmetric connection Gamma which are originally assumed unrelated. It then derives sufficient conditions on h and Gamma (expressed through the curvature tensor of Gamma) for Gamma to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

Original language | English |
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Pages (from-to) | 2995-3010 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- GENERAL-RELATIVITY
- CURVATURE COLLINEATIONS
- EINSTEIN SPACES
- HOLONOMY GROUPS
- TERMS
- GIJ

## Cite this

Hall, G. S., & Lonie, D. P. (2006). On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds.

*Journal of Physics A: Mathematical and General*,*39*, 2995-3010. https://doi.org/10.1088/0305-4470/39/12/009