Insufficiency of the Ricci and Bianchi identities for characterising curvature

doi:10.1016/0393-0440(89)90006-5

Journal of Geometry and Physics

Volume 6, Issue 1, 1989, Pages 159-163

https://doi.org/10.1016/0393-0440(89)90006-5 Get rights and content

Abstract

The status of the Bianchi and Ricci identities as integrability conditions for the existence of a metric having a given tensor as Riemann curvature tensor is discussed. That these identities do not suffice to characterise curvature is shown by means of examples. Similar considerations apply to curvature forms in gauge theories.

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Algebraic determination of the metric from the curvature in General Relativity
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There are more references available in the full text version of this article.

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Insufficiency of the Ricci and Bianchi identities for characterising curvature

Abstract

Metrics with prescribed Ricci curvature

Dynamics of pressure-free matter in General Relativity

J. Math. Phys.

Algebraic determination of the metric from the curvature in General Relativity

Int. J. Theor. Phys.