Remarks on compact spacelike hypersurfaces in de Sitter space with constant higher order mean curvature

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 one of the mean curvatures H l does not vanish and the ratio H k / H l is constant for some k, l, 1≤ l< k≤ n. This extends the previous result in [J. Geom. Phys. 31 (1999) 195, Theorem 7].