  A spacetime manifold \(M\) is a “projective manifold”  (M, \(\Pi)\), if in addition to its manifold structure (differential  topological structure), it is also endowed with a projective structure \(\Pi\) that assigns to each of its manifold points 64 coefficients  \(\Pi^{\,i}_{jk} x^{i}(p))\) satisfying certain symmetry   conditions.[42]  These projective coefficients characterize the equivalence class  [\(\Gamma\)] of projectively equivalent connections, that is,  connections equivalent under the projective transformation  (7). 