Projective manifolds and projective theory of relativity

We present a global formulation of projective theories of relativity in the framework of projective manifolds, that is, manifolds based on the pseudogroup of homogeneous transformations in $R5.$ Apart from formulating every previously considered geometric object and physical relation in an invariant manner, some new results, such as the theorem on the semidirect product structure of the invariance group of Einstein‐Maxwell equations, and theorems on topological restrictions on the underlying five‐dimensional projective manifold, etc. have been obtained. The relationship between space‐time and the auxiliary 5‐manifold is clarified and investigated in detail. A more general geometric definition of the electromagnetic field tensor and a geometric interpretation of the charge/mass ratio is given.