  The purpose of this article is twofold. First we give a very robust method
for proving sharp time decay estimates for the most classical three models of
dispersive Partial Differential Equations, the wave, Klein-Gordon and
Schr{\"o}dinger equations, on curved geometries, showing under very general
assumptions the exact same decay as for the Euclidean case. Then we also extend
these decay properties to the case of boundary value problems.
