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

Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations