Published online by Cambridge University Press: 24 October 2008
A collineation in a space of paths is defined as a point transformation which carries paths into paths. Such transformations were first studied by L. P. Eisenhart and M. S. Knebelman. Subsequently J. Douglas introduced the geometry of K-spreads and E. T. Davies has shown that the results for an affine space of paths can be extended to these more general spaces and written in a very elegant form by the aid of Lie derivation.