Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-01-01

Journal: BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE

Included Journals: SCIE

Volume: 60

Issue: 1

Page Number: 33-49

ISSN: 1220-3874

Key Words: Lorentzian warped product; warping function; complete hyper surface; higher order mean curvature; spacelike slice

Abstract: In this paper, we apply several forms of generalized maximum principles to study the uniqueness of complete spacelike hypersurfaces immersed in Lorentzian warped products. First, we consider the cases of ambient space with vanish f', then obtain some uniqueness results of constant k-th mean curvature. Afterwards, we obtain the sign relationship between the support function with the derivative of warping function. By using this result, under some suitable restriction on the higher order mean curvature, we establish the uniqueness results of Lorentzian warped product -R x (f) M-n with non-vanish f'. Furthermore, applications to such spaces are given.