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Zbl 0661.53017
Hall, G.S.; da Costa, J.
Affine collineations in space-time.
(English)
[J] J. Math. Phys. 29, No. 11, 2465-2472 (1988). ISSN 0022-2488; ISSN 1089-7658/e

Local Lie groups of local affine transformations are considered. The defining condition $\xi\sb{a;bc}=R\sb{abcd}\xi\sp d$ is evaluated, and the connection to the possible different types of the holonomy group (discussed in an earlier paper of the first author and {\it 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.
[H.Stephani]
MSC 2000:
*53B30 Lorentz metrics, indefinite metrics
83C99 General relativity

Keywords: holonomy group; non-flat space-times; affine collineations

Citations: Zbl 0645.53012

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