Abstract
Given a generalized M ¯ n + 1 = I × ϕ F n Robertson–Walker spacetime whose warping function verifies a certain convexity condition, we classify strongly stable spacelike hypersurfaces with constant mean curvature. More precisely, we will show that given x : M n → M ¯ n + 1 a closed, strongly stable spacelike hypersurface of M ¯ n + 1 with constant mean curvature H, if the warping function ϕ satisfying ϕ ″ ⩾ max { H ϕ ′ , 0 } along M, then M n is either maximal or a spacelike slice M t 0 = { t 0 } × F , for some t 0 ∈ I .
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