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Complete hypersurfaces immersed in a semi-Riemannian warped product. (English) Zbl 1238.53035
The authors investigate the uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product space of \(n\) dimensions in the case when the warping function has a convex logarithm and a fiber of constant sectional curvature. They establish that under certain conditions such a hypersurface is a slice.
Contents include: Introduction; Riemannian immersions in semi-Riemannian manifolds; Semi-Riemannian warped products; Proofs of Theorems 1.1 and 1.2 and their corollaries; References (twenty-five items).

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53B20 Local Riemannian geometry
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53Z05 Applications of differential geometry to physics
83C99 General relativity
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