Abstract
It is shown that a compact spacelike hypersurface contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if there exist nonnegative constants C1,C2,…,Cl−1, at least one Ci is positive, such that Hl=∑i=1l−1CiHi.This extends the previous result in [J. Geom. Phys. 39 (2001), Theorem 2].
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