We describe how the deformation matrix $\Omega ^{\mu}_{\nu}$, which relates the sources of matter associated with the metric $g_{\mu\nu}$ and the metric $q_{\mu\nu}$, provides an alternative description for the Einstein tensor, relating it to the energy-moment tensor $\tilde{T}^{\mu}_{\nu}(q) $. We will use gravity $f(R)$ to establish the general mapping equations for scalar fields.