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Uniqueness of complete hypersurfaces with bounded higher order mean curvatures in semi-Riemannian warped products. (English) Zbl 1242.53065
This paper aims uniqueness results for complete hypersurfaces immersed into warped products of type ±× e t M n with certain curvature restrictions. The key assumption is that the hypersurface satisfies 0<βH r H r+1 α for two constants α, β where H r denotes the r-th mean curvature. The conclusion is that the hypersurface is a slice in the warped product. This continues previous work by the authors in [Differ. Geom. Appl. 29, No. 4, 590–596 (2011; Zbl 1219.53056)] and by A. Caminha and the second author in [Gen. Relativ. Gravitation 41, No. 1, 173–189 (2009; Zbl 1162.83304)]. One of the ingredients in each case is Yau’s square operator.
MSC:
53C42Immersions (differential geometry)
53B30Lorentz metrics, indefinite metrics
53C50Lorentz manifolds, manifolds with indefinite metrics
53Z05Applications of differential geometry to physics
83C99General relativity