Abstract
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.
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C. Aquino is partially supported by CNPq/Brazil, grant 302738/2014-2.
H. Baltazar is partially supported by CNPq/Brazil.
H.F. de Lima is partially supported by CNPq/Brazil, grant 303977/2015-9.
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Aquino, C., Baltazar, H. & de Lima, H. A New Calabi–Bernstein Type Result in Spatially Closed Generalized Robertson–Walker Spacetimes. Milan J. Math. 85, 235–245 (2017). https://doi.org/10.1007/s00032-017-0271-z
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DOI: https://doi.org/10.1007/s00032-017-0271-z