Biconservative Surfaces in Robertson-Walker Spaces

In this paper, we mainly focus on space-like PMCV surfaces in Robertson-Walker spacetimes. First, we derive certain geometrical properties of biconservative surfaces in the Robertson-Walker space Lⁿ₁(f, c) of arbitrary dimension. Then, we get complete local classifications of such surfaces in L⁴₁(f,0), L⁵₁(f,0) and L⁵₁(1,± 1). Finally, we proved that a space-like PMCV biconservative surface in Lⁿ₁(f,0) lies on a totally geodesic submanifold with dimension $4$ or $5$.