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Stable space-like hypersurfaces in the de Sitter space. (English) Zbl 1114.53057

Using the viewpoints of the calculus of variation, the authors study the stability of space-like hypersurfaces with constant scalar curvature immersed in de Sitter spaces.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53B25 Local submanifolds
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