CMC biconservative surfaces in $\mathbb{S}^n\times\mathbb{R}$ and   $\mathbb{H}^n\times\mathbb{R}$
  We classify non-minimal biconservative surfaces with parallel mean curvature vector field in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$. When these surfaces do not lie in $\mathbb{S}^n$ or $\mathbb{H}^n$ and they are not vertical cylinders, we find their explicit (local) equation. We also prove a result on the compactness of biconservative surfaces with constant mean curvature in Hadamard manifolds. 
Dorel Fetcu, Cezar Oniciuc, and Ana Lucia Pinheiro
math.DG