Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations

We investigate the relation of Lie point symmetries for geodesic equations with collineations decomposable spacetimes. review previous results in literature on and we follow a proposed geometric construction approach differential equations. In this study prove that projective $\left( n+1\right) \,$% -dimensional Riemannian space are $n$-dimensional subspace. demonstrate application our presentation applications.