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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 ξ a;bc =R abcd ξ 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:
53B30Lorentz metrics, indefinite metrics
83C99General relativity