In this paper, we characterize static perfect fluid spacetimes on almost co-Kähler manifolds. At first, it is shown that if a [Formula: see text]-almost co-Kähler manifold [Formula: see text] is the spatial factor of a static perfect fluid spacetime, then [Formula: see text] is either a [Formula: see text]-almost co-Kähler manifold or Ricci flat. Next, we consider the case for a 3-dimensional co-Kähler manifold [Formula: see text] as the spatial factor of a static perfect fluid spacetime.
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De et al. (2024) studied this question.
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