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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.
Turgay et al. (Thu,) studied this question.