Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product

Wang, Yaning; Liu, Ximin

doi:10.1515/auom-2015-0041

Abstract

In this paper, by supposing a natural comparison inequality on the positive r-th mean curvatures of the hypersurface, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces immersed in a semi-Riemannian warped product of constant sectional curvature. Generalizing the above results, under a restriction on the sectional curvature or the Ricci curvature tensor of the fiber of a warped product, we also prove some new rigidity theorems in semi-Riemannian warped products. Our main results extend some recent Bernstein-type theorems proved in [12, 13, 14].

References

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Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product

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