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A New Characterization of Totally Umbilical Hypersurfaces in de Sitter Space

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DOI: 10.4236/apm.2014.42006    2,644 Downloads   3,795 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Cao, G. Xu and Z. Dai, "A New Characterization of Totally Umbilical Hypersurfaces in de Sitter Space," Advances in Pure Mathematics, Vol. 4 No. 2, 2014, pp. 42-46. doi: 10.4236/apm.2014.42006.

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