A New Characterization of Totally Umbilical Hypersurfaces in de Sitter Space

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2014Publisher:Scientific Research Publishing, Inc.Journal:Advances in Pure Mathematics, volume 4, pages 42-46 (issn: 2160-0368, eissn: 2160-0384,

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Authors: Linfen Cao; Guodong Xu; Zhaohui Dai;

doi: 10.4236/apm.2014.42006

A New Characterization of Totally Umbilical Hypersurfaces in de Sitter Space

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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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Henan Normal University
China (People's Republic of)

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