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Indexed by:期刊论文

Date of Publication:2015-01-01

Journal:ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA

Included Journals:SCIE、Scopus

Volume:23

Issue:2

Page Number:259-277

ISSN No.:1224-1784

Key Words:Complete spacelike hypersurface; semi-Riemannian warped product; r-th mean curvature; Bernstein-type theorem

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].