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