  We consider a problem of prescribing the partial Ricci curvature on a locally
conformally flat manifold $(M^n, g)$ endowed with the complementary orthogonal
distributions $D_1$ and $D_2$. We provide conditions for symmetric
$(0,2)$-tensors $T$ of a simple form (defined on $M$) to admit metrics $\tilde
g$, conformal to $g$, that solve the partial Ricci equations. The solutions are
given explicitly. Using above solutions, we also give examples to the problem
of prescribing the mixed scalar curvature related to $D_i$. In aim to find
"optimally placed" distributions, we calculate the variations of the total
mixed scalar curvature (where again the partial Ricci curvature plays a key
role), and give examples concerning minimization of a total energy and bending
of a distribution.
