Ricci Tensors with Rotational Symmetry on R^n
  In this paper is considered the differential equation Ric(g)=T, where Ric(g) is the Ricci tensor of the metric g and T is a rotational symmetric tensor on R^n. A new, geometric, proof of the existence of smooth solutions of this equation, based on qualitative theory of implicitdifferential equations, is presented here. This result was obtained previously by DeTurck and Cao in 1994. 
Ronaldo Garcia and Romildo Pina