Abstract
This is a reprinting of the paper by Jurgen Ehlers, Felix Pirani and Alfred Schild, first published in 1972 in a separate volume containing articles written in hounour of J. L. Synge. The original book is long out of print and almost forgotten by today. The authors present a method of deriving the Lorentzian geometry from compatible conformal and projective structures on a four dimensional manifold. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Andrzej Trautman.
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