Static perfect fluid spacetimes on f-Kenmotsu 3-manifolds

期刊论文
发表日期：

2024年12月5日

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Uday Chand De,
Arpan Sardar

摘要

The present article deals with static perfect fluid spacetimes on f-Kenmotsu 3-manifolds. At first, we demonstrate if a 3-dimensional f-Kenmotsu manifold with constant scalar curvature as the spatial factor of a static perfect fluid spacetime, then either it is a space of constant sectional curvature or $grad\, \psi $ $g r a d ψ$ is pointwise collinear with $\xi $ $ξ$ and the warping function of the static perfect fluid spacetime is given by $\psi = k_1 t + k_2$ $ψ = k_{1} t + k_{2}$ , $k_1 \ne 0$ $k_{1} \neq 0$ . As a result, we establish that if a cosymplectic manifold of dimension three with constant scalar curvature is the spatial factor of a static perfect fluid spacetime, then either it is flat or, the manifold becomes a space of constant sectional curvature. Next, we show that under certain restrictions if a 3-dimensional f-Kenmotsu manifold is the spatial factor of a static perfect fluid spacetime, then either the manifold is a space of constant sectional curvature or, the manifold is locally isometric to either the flat Euclidean space $\mathcal {R}^3$ $R^{3}$ or the Riemannian product $\mathcal {R}\times M^2(c)$ $R \times M^{2} (c)$ , where $M^2(c)$ $M^{2} (c)$ represents a Kahler surface with constant curvature $c\ne 0$ $c \neq 0$ , provided $\xi \psi =0$ $ξ ψ = 0$ and $\xi \tilde{f} =0$ $ξ \tilde{f} = 0$ . Lastly, we have cited an example of an f-Kenmotsu manifold to validate our result.