Abstract

In this paper, we prove that minimal hypersurfaces when n <TEX>$\geq$</TEX> 3 and nonzero constant mean curvature hypersurfaces when n <TEX>$\geq$</TEX> 2 foliated by spheres in parallel horizontal hyperplanes in <TEX>$\mathbb{H}^n{\times}\mathbb{R}$</TEX> must be rotationally symmetric.

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