On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds

Graham Stanley Hall; D. P. Lonie

doi:10.1088/0305-4470/39/12/009

On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds

Graham Stanley Hall, D. P. Lonie

Mathematical Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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
Pages (from-to)	2995-3010
Number of pages	15
Journal	Journal of Physics A: Mathematical and General
Volume	39
DOIs	https://doi.org/10.1088/0305-4470/39/12/009
Publication status	Published - 2006

Keywords

GENERAL-RELATIVITY
CURVATURE COLLINEATIONS
EINSTEIN SPACES
HOLONOMY GROUPS
TERMS
GIJ

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10.1088/0305-4470/39/12/009

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title = "On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds",

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.",

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AU - Lonie, D. P.

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N2 - 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.

AB - 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.

KW - GENERAL-RELATIVITY

KW - CURVATURE COLLINEATIONS

KW - EINSTEIN SPACES

KW - HOLONOMY GROUPS

KW - TERMS

KW - GIJ

U2 - 10.1088/0305-4470/39/12/009

DO - 10.1088/0305-4470/39/12/009

M3 - Article

SN - 0305-4470

VL - 39

SP - 2995

EP - 3010

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

ER -

On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds

Abstract

Keywords

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