  We obtain the fully covariant linearized field equations for the metric
perturbation in the de Rham-Gabadadze-Tolley (dRGT) ghost free massive
gravities. For a subset of these theories, we show that the non dynamical
metric that appears in the dRGT setup can be completely eliminated leading to
the theory of a massive graviton moving in a single metric. This has a mass
term which contains non trivial contributions of the space-time curvature. We
show further how 5 covariant constraints can be obtained including one which
leads to the tracelessness of the graviton on flat space-time and removes the
Boulware-Deser ghost. The 5 constraints are obtained for a background metric
which is arbitrary, i.e. which does not have to obey the background field
equations.
