On the rescaling problem of space-times admitting groups of conformal motions

Recent developments in the investigations connected with quantum field theory in curved spacetimes, the large scale structure of the Universe revealed a possible relevance of conformal analogous of the theory of general relativity. In such theories the role of Killing symmetries of the conventional Einstein theory is shifted to that of conformal Killing symmetries. In the paper it is supposed that a spacetime manifold admits a group of conformal symmetries and an answer is given to the question of the necessary and sufficient conditions the manifold and the generators has to fulfil in order that the manifold be conformally equivalent to a spacetime admitting the same group but of ordinary Killing symmetries. (Sz.N.Z.)