Biconservative Surfaces in Robertson-Walker Spaces

In this paper, we mainly focus on space-like PMCV surfaces in Robertson-Walker spaces. First, we derive certain geometrical properties of biconservative surfaces in the Robertson-Walker space L-1(n)(f,c) of arbitrary dimension. Then, we get complete local classifications of PMCV surfaces in L-1(4)(f,0), L15(f,0) and L-1(5)(1,+/- 1). Finally, we prove that a space-like PMCV biconservative surface in L-1(n)(f,0), n >= 6 lies on a totally geodesic submanifold with dimension either 4 or 5.