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Some rigidity theorems in semi-Riemannian warped products. (English) Zbl 1252.53068
The authors study the problem of uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product, whose warping function has convex logarithm. By applying a maximum principle at infinity and supposing a natural comparison inequality between the mean curvature of the hypersurface and that of the slices of the region in which the hypersurface is contained, they obtain rigidity theorems in such ambient spaces. Applications are also given.

53C42Immersions (differential geometry)
53B30Lorentz metrics, indefinite metrics
53C50Lorentz manifolds, manifolds with indefinite metrics
53Z05Applications of differential geometry to physics
83C99General relativity
53C24Rigidity results (differential geometry)
Full Text: DOI Euclid