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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
##### Keywords:
holonomy group; non-flat space-times; affine collineations
Zbl 0645.53012
Full Text:
##### References:
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