CMC biconservative surfaces in Sn×RSn×R and Hn×RHn×R

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in Sn×RSn×R and Hn×RHn×R. When these surfaces do not lie in SnSn or HnHn 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.