AFFINE COLLINEATIONS IN GENERAL-RELATIVITY AND THEIR FIXED-POINT STRUCTURE

A general discussion of affine vector fields (collineations) in space- time is given following a previous article by Hall and da Costa. Some general remarks are presented on the zeros of affine vector fields and then the general theory of such zeros is established. Some preliminar y results regarding homothetic symmetries in two-and three-dimensional space-times are also given. The impossibility of reducing an affine a lgebra containing proper affine vector fields to homothetic or Killing vector fields, by means of a change of compatible metric, is demonstr ated.