Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2001-07-01

Journal: MANUSCRIPTA MATHEMATICA

Included Journals: SCIE、Scopus

Volume: 105

Issue: 3

Page Number: 367-377

ISSN: 0025-2611

Abstract: Let M-n be a complete space-like hypersurface with constant normalized scalar curvature R in the de Sitter space S-1(n+1) and denote (R) over bar = 1 - R. We prove that if the norm square \h\(2) of the second fundamental form of M-n satisfies n (R) over bar less than or equal to sup \h\(2) less than or equal to n/(n-2)(n (R$) over bar -2)[n(n - 1)(R) over bar (2) - 4(n - 1)(R) over bar + n], then either sup \h\(2) = n (R) over bar and M-n is a totally umbilical hypersurface; or sup \h\(2) = n/(n-2)(n (R) over bar -2)[n(n - 1)(R) over bar (2) - 4(n - 1)(R) over bar + n], and, up to rigid motion, M-n is a hyperbolic cylinder H-1(1 - coth(2) r) X Sn-1(1 - tanh(2) r).