Abstract
Although curvature collineations (curvature preserving transformations) have been studied within the context of general relativity for 20 years, there has been little attempt to study them systematically and there does not appear to have been a detailed mathematical investigation of their properties. This is the first of two papers that are intended as a contribution to this deficiency. This paper presents a discussion of the more general mathematical aspects of curvature collineations and suggests a program for studying them. The implementation of this program and the analysis of specific examples will be carried out in the second paper.
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