On biconservative surfaces in 3-dimensional space forms

We consider biconservative surfaces $(M^2,g)$ in a space form $N^3(c)$, with mean curvature function $f$ satisfying $f>0$ and $\nabla f\neq 0$atanypoint,anddetermineacertainRiemannianmetric$g_r$on$M$ such that $(M^2,g_r)$ is a Ricci surface in $N^3(c)$. We also obtain an intrinsic characterization of these biconservative surfaces.