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Affine collineations in space-time. (English) Zbl 0661.53017
Local Lie groups of local affine transformations are considered. The defining condition \(\xi_{a;bc}=R_{abcd}\xi^ d\) is evaluated, and the connection to the possible different types of the holonomy group (discussed in an earlier paper of the first author and W. Kay [ibid. 29, No.2, 428-432 (1988; Zbl 0645.53012)] is established. For non- flat space-times, the maximum dimension of the Lie algebra turns out to be 9. Fixed points and global extensions of affine collineations are discussed.
Reviewer: H.Stephani

MSC:
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83C99 General relativity
Citations:
Zbl 0645.53012
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References:
[1] DOI: 10.1007/BF00758964 · Zbl 0642.53027
[2] DOI: 10.1063/1.528031 · Zbl 0645.53012
[3] DOI: 10.1063/1.1703700 · Zbl 0096.21903
[4] Wu H., Illinois J. Math. 8 pp 291– (1964)
[5] DOI: 10.1063/1.528030 · Zbl 0651.53017
[6] DOI: 10.1063/1.525483 · Zbl 0489.53031
[7] DOI: 10.1088/0305-4470/9/4/010 · Zbl 0326.15009
[8] DOI: 10.1007/BF00758972 · Zbl 0646.53024
[9] DOI: 10.2307/1970148 · Zbl 0093.35103
[10] DOI: 10.1007/BF00419621 · Zbl 0394.53035
[11] DOI: 10.1007/BF01610003 · Zbl 0322.53008
[12] DOI: 10.1063/1.527903 · Zbl 0649.53012
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