A New Characterization of Totally Umbilical Hypersurfaces in de Sitter Space

DOI: 10.4236/apm.2014.42006   PDF   HTML     2,744 Downloads   3,965 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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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