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Holonomy groups in general relativity. (English) Zbl 0645.53012
The infinitesimal holonomy group structure of space-time is discussed and related to the Petrov type of the Weyl tensor and the algebraic type of the energy-momentum tensor, and a list of all possible groups is given. It turns out that, in determining the holonomy group, at most the second derivatives of the curvature tensor need to be considered.
Reviewer: H.Stephani

MSC:
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83C99 General relativity
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