The aim of this article is to study the uniqueness of a complete spacelike hypersurface \({\sum^{n}}\) immersed with constant mean curvature H in a spatially closed generalized Robertson–Walker spacetime \({\overline{M}^{n+1} = -I {\times_{f}} {M^{n}}}\), whose Riemannian fiber \({M^n}\) has positive curvature. Supposing that the warping function f is such that −log f is convex and \({H{f^{\prime}} \leq 0}\) along \({\sum^{n}}\), we show that \({\sum^{n}}\) must be isometric to a totally geodesic slice of \({\overline{M}^{n+1}}\). When \({\overline{M}^{n+1}}\) is a Lorentzian product space, we obtain a new Calabi–Bernstein type result concerning the CMC spacelike hypersurface equation.

中文翻译：

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空间闭合广义罗伯逊-沃克时空的新Calabi-Bernstein类型结果

本文的目的是研究浸没在恒定的平均曲率H下的完整空间状超曲面\（{\ sum ^ {n}} \）的唯一性，该空间闭合广义Robertson-Walker时空\（{\ overline {M} ^ {n + 1} = -I {\ times {{f}} {M ^ {n}}} \），其黎曼纤维\（{M ^ n} \）具有正曲率。假设翘曲函数f使得-log f是凸的并且沿着\（{\ sum ^ {n}} \）\\ {{H {f ^ {\ prime}} \ leq 0 } \），我们证明\（{\ sum ^ {n}} \）必须与\（{\ overline {M} ^ {n + 1}} \\）的完全测地切片等轴测。当\（{\ overline {M} ^ {n + 1}} \） 是一个洛伦兹积空间，我们获得了有关CMC类空超曲面方程的新Calabi–Bernstein型结果。