TITLE:
A New Characterization of Totally Umbilical Hypersurfaces in de Sitter Space
AUTHORS:
Linfen Cao, Guodong Xu, Zhaohui Dai
KEYWORDS:
de Sitter Space; Spacelike Hypersurface; Higher Order Mean Curvatures
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.2,
February
24,
2014
ABSTRACT: It is shown that a compact spacelike hypersurface which is contained
in the chronological future (or past) of an equator of de Sitter space is a
totally umbilical round sphere if the kth
mean curvature function Hk is a linear combination of Hk+1,…, Hn. This is a new angle to characterize round spheres.