  It is shown that any theory of gravitation, based on the hypothesis of the
geodesic motion of test particles must be invariant under geodesic (projecive)
mappings of the used space-time. The reason is that due to invariance of the
equations of geodesic lines under a continuous group of transformations of the
coefficients of affine connection, there is a wide class of transformations of
the geometrical objects of Riemannian space-time which leaves invariant the
equations of motion of test particles. The FRW metric in cosmology and the
Schwarzschild metric are a good example to make sure that the standard
space-time metrics does not determine the gravitational field unequivocally.
