Static perfect fluid spaces are of great interest in metric theories of gravitation, they being used in building realistic models of some compact objects, like neutron stars and white dwarfs. In this article, we show that a compact static perfect fluid space with non-trivial solution f and Ricci curvature in the direction of the vector field $\mathrm{grad}f$ bounded below by a certain lower bound, is necessarily a standard sphere and the converse statement also holds. Moreover, we establish two simple characterizations of the Euclidean spaces through connected static perfect fluid spaces.

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关于静态空间的说明

静态完美流体空间对引力度量理论非常感兴趣，它们被用于构建一些紧凑物体的真实模型，如中子星和白矮星。在本文中，我们展示了在矢量场方向上具有非平凡解f和 Ricci 曲率的紧凑静态完美流体空间$\mathrm{研究生}F$以某个下界为界，必然是一个标准球体，逆命题也成立。此外，我们通过连接的静态完美流体空间建立了欧几里德空间的两个简单表征。