Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-01-01

Journal: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA

Included Journals: Scopus、SCIE

Volume: 23

Issue: 2

Page Number: 259-277

ISSN: 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].