Abstract
This paper aims at discussing two issues that can have a big impact on our understanding of properties of space-time and gravitation: 1)The existence of relativity of space-time geometry with respect to the properties of used reference frame, which in fact follows from the well-known fact of relativity of geometry of space and time with respect to properties of measuring instruments (Henri Poincaré). 2)The existence of the fact that the equations of motion of test particles in general relativity are invariant under a continuous group of geodesic (projective) maps of the metric tensor, and therefore they should play a role of gauge transformations in any theory of gravitation based on the hypothesis of the geodesic motion of free particles. Classical Einstein's equations are not invariant under these maps.
Leonid V. Vebrozub