This paper aims uniqueness results for complete hypersurfaces immersed into warped products of type
with certain curvature restrictions. The key assumption is that the hypersurface satisfies
for two constants
-th mean curvature. The conclusion is that the hypersurface is a slice in the warped product. This continues previous work by the authors in [Differ. Geom. Appl. 29, No. 4, 590–596 (2011; Zbl 1219.53056
)] and by A. Caminha
and the second author in [Gen. Relativ. Gravitation 41, No. 1, 173–189 (2009; Zbl 1162.83304
)]. One of the ingredients in each case is Yau’s square operator.